diff --git a/source/reduce/CMakeLists.txt b/source/reduce/CMakeLists.txt
index 57475ac5e..0a6bce99c 100644
--- a/source/reduce/CMakeLists.txt
+++ b/source/reduce/CMakeLists.txt
@@ -13,11 +13,14 @@
 # limitations under the License.
 set(SPIRV_TOOLS_REDUCE_SOURCES
         change_operand_reduction_opportunity.h
+        change_operand_to_undef_reduction_opportunity.h
         operand_to_const_reduction_pass.h
+        operand_to_undef_reduction_pass.h
         operand_to_dominating_id_reduction_pass.h
         reducer.h
         reduction_opportunity.h
         reduction_pass.h
+        reduction_util.h
         remove_instruction_reduction_opportunity.h
         remove_opname_instruction_reduction_pass.h
         remove_unreferenced_instruction_reduction_pass.h
@@ -25,11 +28,14 @@ set(SPIRV_TOOLS_REDUCE_SOURCES
         structured_loop_to_selection_reduction_pass.h
 
         change_operand_reduction_opportunity.cpp
+        change_operand_to_undef_reduction_opportunity.cpp
         operand_to_const_reduction_pass.cpp
+        operand_to_undef_reduction_pass.cpp
         operand_to_dominating_id_reduction_pass.cpp
         reducer.cpp
         reduction_opportunity.cpp
         reduction_pass.cpp
+        reduction_util.cpp
         remove_instruction_reduction_opportunity.cpp
         remove_unreferenced_instruction_reduction_pass.cpp
         remove_opname_instruction_reduction_pass.cpp
diff --git a/source/reduce/change_operand_reduction_opportunity.h b/source/reduce/change_operand_reduction_opportunity.h
index 9e43ec969..7e1fc8e3b 100644
--- a/source/reduce/change_operand_reduction_opportunity.h
+++ b/source/reduce/change_operand_reduction_opportunity.h
@@ -24,8 +24,7 @@ namespace reduce {
 
 using namespace opt;
 
-// Captures the opportunity to change an id operand of an instruction to some
-// other id.
+// An opportunity to replace an id operand of an instruction with some other id.
 class ChangeOperandReductionOpportunity : public ReductionOpportunity {
  public:
   // Constructs the opportunity to replace operand |operand_index| of |inst|
@@ -38,13 +37,9 @@ class ChangeOperandReductionOpportunity : public ReductionOpportunity {
         original_type_(inst->GetOperand(operand_index).type),
         new_id_(new_id) {}
 
-  // Determines whether the opportunity can be applied; it may have been viable
-  // when discovered but later disabled by the application of some other
-  // reduction opportunity.
   bool PreconditionHolds() override;
 
  protected:
-  // Apply the change of operand.
   void Apply() override;
 
  private:
diff --git a/source/reduce/change_operand_to_undef_reduction_opportunity.cpp b/source/reduce/change_operand_to_undef_reduction_opportunity.cpp
new file mode 100644
index 000000000..8e33da661
--- /dev/null
+++ b/source/reduce/change_operand_to_undef_reduction_opportunity.cpp
@@ -0,0 +1,41 @@
+// Copyright (c) 2018 Google LLC
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "source/reduce/change_operand_to_undef_reduction_opportunity.h"
+
+#include "source/opt/ir_context.h"
+#include "source/reduce/reduction_util.h"
+
+namespace spvtools {
+namespace reduce {
+
+bool ChangeOperandToUndefReductionOpportunity::PreconditionHolds() {
+  // Check that the instruction still has the original operand.
+  return inst_->NumOperands() > operand_index_ &&
+         inst_->GetOperand(operand_index_).words[0] == original_id_;
+}
+
+void ChangeOperandToUndefReductionOpportunity::Apply() {
+  auto operand = inst_->GetOperand(operand_index_);
+  auto operand_id = operand.words[0];
+  auto operand_id_def = context_->get_def_use_mgr()->GetDef(operand_id);
+  auto operand_type_id = operand_id_def->type_id();
+  // The opportunity should not exist unless this holds.
+  assert(operand_type_id);
+  auto undef_id = FindOrCreateGlobalUndef(context_, operand_type_id);
+  inst_->SetOperand(operand_index_, {undef_id});
+}
+
+}  // namespace reduce
+}  // namespace spvtools
diff --git a/source/reduce/change_operand_to_undef_reduction_opportunity.h b/source/reduce/change_operand_to_undef_reduction_opportunity.h
new file mode 100644
index 000000000..ffd3155b0
--- /dev/null
+++ b/source/reduce/change_operand_to_undef_reduction_opportunity.h
@@ -0,0 +1,53 @@
+// Copyright (c) 2018 Google LLC
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef SOURCE_REDUCE_CHANGE_OPERAND_TO_UNDEF_REDUCTION_OPPORTUNITY_H_
+#define SOURCE_REDUCE_CHANGE_OPERAND_TO_UNDEF_REDUCTION_OPPORTUNITY_H_
+
+#include "source/opt/instruction.h"
+#include "source/reduce/reduction_opportunity.h"
+#include "spirv-tools/libspirv.h"
+
+namespace spvtools {
+namespace reduce {
+
+// An opportunity to replace an id operand of an instruction with undef.
+class ChangeOperandToUndefReductionOpportunity : public ReductionOpportunity {
+ public:
+  // Constructs the opportunity to replace operand |operand_index| of |inst|
+  // with undef.
+  ChangeOperandToUndefReductionOpportunity(opt::IRContext* context,
+                                           opt::Instruction* inst,
+                                           uint32_t operand_index)
+      : context_(context),
+        inst_(inst),
+        operand_index_(operand_index),
+        original_id_(inst->GetOperand(operand_index).words[0]) {}
+
+  bool PreconditionHolds() override;
+
+ protected:
+  void Apply() override;
+
+ private:
+  opt::IRContext* context_;
+  opt::Instruction* const inst_;
+  const uint32_t operand_index_;
+  const uint32_t original_id_;
+};
+
+}  // namespace reduce
+}  // namespace spvtools
+
+#endif  // SOURCE_REDUCE_CHANGE_OPERAND_TO_UNDEF_REDUCTION_OPPORTUNITY_H_
diff --git a/source/reduce/operand_to_const_reduction_pass.cpp b/source/reduce/operand_to_const_reduction_pass.cpp
index 35c0f4bee..4d04506e1 100644
--- a/source/reduce/operand_to_const_reduction_pass.cpp
+++ b/source/reduce/operand_to_const_reduction_pass.cpp
@@ -12,9 +12,10 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "operand_to_const_reduction_pass.h"
-#include "change_operand_reduction_opportunity.h"
+#include "source/reduce/operand_to_const_reduction_pass.h"
+
 #include "source/opt/instruction.h"
+#include "source/reduce/change_operand_reduction_opportunity.h"
 
 namespace spvtools {
 namespace reduce {
diff --git a/source/reduce/operand_to_const_reduction_pass.h b/source/reduce/operand_to_const_reduction_pass.h
index fd7cfa006..4e7381e93 100644
--- a/source/reduce/operand_to_const_reduction_pass.h
+++ b/source/reduce/operand_to_const_reduction_pass.h
@@ -15,12 +15,12 @@
 #ifndef SOURCE_REDUCE_OPERAND_TO_CONST_REDUCTION_PASS_H_
 #define SOURCE_REDUCE_OPERAND_TO_CONST_REDUCTION_PASS_H_
 
-#include "reduction_pass.h"
+#include "source/reduce/reduction_pass.h"
 
 namespace spvtools {
 namespace reduce {
 
-// A reduction pass for turning id operands of instructions into ids of
+// A reduction pass for replacing id operands of instructions with ids of
 // constants.  This reduces the extent to which ids of non-constants are used,
 // paving the way for instructions that generate them to be eliminated by other
 // passes.
@@ -33,12 +33,9 @@ class OperandToConstReductionPass : public ReductionPass {
 
   ~OperandToConstReductionPass() override = default;
 
-  // The name of this pass.
   std::string GetName() const final;
 
  protected:
-  // Finds all opportunities for replacing an operand with a constant in the
-  // given module.
   std::vector<std::unique_ptr<ReductionOpportunity>> GetAvailableOpportunities(
       opt::IRContext* context) const final;
 
diff --git a/source/reduce/operand_to_dominating_id_reduction_pass.h b/source/reduce/operand_to_dominating_id_reduction_pass.h
index b62b6ae32..36bb20112 100644
--- a/source/reduce/operand_to_dominating_id_reduction_pass.h
+++ b/source/reduce/operand_to_dominating_id_reduction_pass.h
@@ -39,12 +39,9 @@ class OperandToDominatingIdReductionPass : public ReductionPass {
 
   ~OperandToDominatingIdReductionPass() override = default;
 
-  // The name of this pass.
   std::string GetName() const final;
 
  protected:
-  // Finds all opportunities for replacing an operand with a dominating
-  // instruction in a given module.
   std::vector<std::unique_ptr<ReductionOpportunity>> GetAvailableOpportunities(
       opt::IRContext* context) const final;
 
diff --git a/source/reduce/operand_to_undef_reduction_pass.cpp b/source/reduce/operand_to_undef_reduction_pass.cpp
new file mode 100644
index 000000000..e3d8a8ea3
--- /dev/null
+++ b/source/reduce/operand_to_undef_reduction_pass.cpp
@@ -0,0 +1,94 @@
+// Copyright (c) 2018 Google LLC
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "source/reduce/operand_to_undef_reduction_pass.h"
+
+#include "source/opt/instruction.h"
+#include "source/reduce/change_operand_to_undef_reduction_opportunity.h"
+
+namespace spvtools {
+namespace reduce {
+
+using namespace opt;
+
+std::vector<std::unique_ptr<ReductionOpportunity>>
+OperandToUndefReductionPass::GetAvailableOpportunities(
+    IRContext* context) const {
+  std::vector<std::unique_ptr<ReductionOpportunity>> result;
+
+  for (auto& function : *context->module()) {
+    for (auto& block : function) {
+      for (auto& inst : block) {
+        // Skip instructions that result in a pointer type.
+        auto type_id = inst.type_id();
+        if (type_id) {
+          auto type_id_def = context->get_def_use_mgr()->GetDef(type_id);
+          if (type_id_def->opcode() == SpvOpTypePointer) {
+            continue;
+          }
+        }
+
+        // We iterate through the operands using an explicit index (rather
+        // than using a lambda) so that we use said index in the construction
+        // of a ChangeOperandToUndefReductionOpportunity
+        for (uint32_t index = 0; index < inst.NumOperands(); index++) {
+          const auto& operand = inst.GetOperand(index);
+
+          if (spvIsInIdType(operand.type)) {
+            const auto operand_id = operand.words[0];
+            auto operand_id_def =
+                context->get_def_use_mgr()->GetDef(operand_id);
+
+            // Skip constant and undef operands.
+            // We always want the reducer to make the module "smaller", which
+            // ensures termination.
+            // Therefore, we assume: id > undef id > constant id.
+            if (spvOpcodeIsConstantOrUndef(operand_id_def->opcode())) {
+              continue;
+            }
+
+            // Don't replace function operands with undef.
+            if (operand_id_def->opcode() == SpvOpFunction) {
+              continue;
+            }
+
+            // Only consider operands that have a type.
+            auto operand_type_id = operand_id_def->type_id();
+            if (operand_type_id) {
+              auto operand_type_id_def =
+                  context->get_def_use_mgr()->GetDef(operand_type_id);
+
+              // Skip pointer operands.
+              if (operand_type_id_def->opcode() == SpvOpTypePointer) {
+                continue;
+              }
+
+              result.push_back(
+                  MakeUnique<ChangeOperandToUndefReductionOpportunity>(
+                      context, &inst, index));
+            }
+          }
+        }
+      }
+    }
+  }
+  return result;
+}
+
+std::string OperandToUndefReductionPass::GetName() const {
+  return "OperandToUndefReductionPass";
+}
+
+}  // namespace reduce
+}  // namespace spvtools
diff --git a/source/reduce/operand_to_undef_reduction_pass.h b/source/reduce/operand_to_undef_reduction_pass.h
new file mode 100644
index 000000000..e4ec603fb
--- /dev/null
+++ b/source/reduce/operand_to_undef_reduction_pass.h
@@ -0,0 +1,45 @@
+// Copyright (c) 2018 Google LLC
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef SOURCE_REDUCE_OPERAND_TO_UNDEF_REDUCTION_PASS_H_
+#define SOURCE_REDUCE_OPERAND_TO_UNDEF_REDUCTION_PASS_H_
+
+#include "source/reduce/reduction_pass.h"
+
+namespace spvtools {
+namespace reduce {
+
+// A reduction pass for replacing id operands of instructions with ids of undef.
+class OperandToUndefReductionPass : public ReductionPass {
+ public:
+  // Creates the reduction pass in the context of the given target environment
+  // |target_env|
+  explicit OperandToUndefReductionPass(const spv_target_env target_env)
+      : ReductionPass(target_env) {}
+
+  ~OperandToUndefReductionPass() override = default;
+
+  std::string GetName() const final;
+
+ protected:
+  std::vector<std::unique_ptr<ReductionOpportunity>> GetAvailableOpportunities(
+      opt::IRContext* context) const final;
+
+ private:
+};
+
+}  // namespace reduce
+}  // namespace spvtools
+
+#endif  // SOURCE_REDUCE_OPERAND_TO_UNDEF_REDUCTION_PASS_H_
diff --git a/source/reduce/reduction_opportunity.h b/source/reduce/reduction_opportunity.h
index da382a2f4..703a50a46 100644
--- a/source/reduce/reduction_opportunity.h
+++ b/source/reduce/reduction_opportunity.h
@@ -20,23 +20,24 @@
 namespace spvtools {
 namespace reduce {
 
-// Abstract class capturing an opportunity to apply a reducing transformation.
+// Abstract class: an opportunity to apply a reducing transformation.
 class ReductionOpportunity {
  public:
   ReductionOpportunity() = default;
   virtual ~ReductionOpportunity() = default;
 
-  // Determines whether the opportunity can be applied; it may have been viable
-  // when discovered but later disabled by the application of some other
-  // reduction opportunity.
+  // Returns true if this opportunity has not been disabled by the application
+  // of another conflicting opportunity.
   virtual bool PreconditionHolds() = 0;
 
-  // A no-op if PreconditoinHolds() returns false; otherwise applies the
-  // opportunity.
+  // Applies the opportunity, mutating the module from which the opportunity was
+  // created. It is a no-op if PreconditionHolds() returns false.
   void TryToApply();
 
  protected:
-  // Apply the reduction opportunity.
+  // Applies the opportunity, mutating the module from which the opportunity was
+  // created.
+  // Precondition: PreconditionHolds() must return true.
   virtual void Apply() = 0;
 };
 
diff --git a/source/reduce/reduction_pass.h b/source/reduce/reduction_pass.h
index afb95cc42..57e1c5f66 100644
--- a/source/reduce/reduction_pass.h
+++ b/source/reduce/reduction_pass.h
@@ -39,13 +39,13 @@ class ReductionPass {
 
   virtual ~ReductionPass() = default;
 
-  // Apply the reduction pass to the given binary.
+  // Applies the reduction pass to the given binary.
   std::vector<uint32_t> TryApplyReduction(const std::vector<uint32_t>& binary);
 
-  // Set a consumer to which relevant messages will be directed.
+  // Sets a consumer to which relevant messages will be directed.
   void SetMessageConsumer(MessageConsumer consumer);
 
-  // Determines whether the granularity with which reduction opportunities are
+  // Returns true if the granularity with which reduction opportunities are
   // applied has reached a minimum.
   bool ReachedMinimumGranularity() const;
 
@@ -54,8 +54,8 @@ class ReductionPass {
   virtual std::string GetName() const = 0;
 
  protected:
-  // Finds the reduction opportunities relevant to this pass that could be
-  // applied to a given SPIR-V module.
+  // Finds and returns the reduction opportunities relevant to this pass that
+  // could be applied to the given SPIR-V module.
   virtual std::vector<std::unique_ptr<ReductionOpportunity>>
   GetAvailableOpportunities(opt::IRContext* context) const = 0;
 
diff --git a/source/reduce/reduction_util.cpp b/source/reduce/reduction_util.cpp
new file mode 100644
index 000000000..103d63f19
--- /dev/null
+++ b/source/reduce/reduction_util.cpp
@@ -0,0 +1,44 @@
+// Copyright (c) 2018 Google LLC
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "source/reduce/reduction_util.h"
+
+#include "source/opt/ir_context.h"
+
+namespace spvtools {
+namespace reduce {
+
+using namespace opt;
+
+uint32_t FindOrCreateGlobalUndef(IRContext* context, uint32_t type_id) {
+  for (auto& inst : context->module()->types_values()) {
+    if (inst.opcode() != SpvOpUndef) {
+      continue;
+    }
+    if (inst.type_id() == type_id) {
+      return inst.result_id();
+    }
+  }
+  // TODO(2182): this is adapted from MemPass::Type2Undef.  In due course it
+  // would be good to factor out this duplication.
+  const uint32_t undef_id = context->TakeNextId();
+  std::unique_ptr<Instruction> undef_inst(
+      new Instruction(context, SpvOpUndef, type_id, undef_id, {}));
+  assert(undef_id == undef_inst->result_id());
+  context->module()->AddGlobalValue(std::move(undef_inst));
+  return undef_id;
+}
+
+}  // namespace reduce
+}  // namespace spvtools
diff --git a/source/reduce/reduction_util.h b/source/reduce/reduction_util.h
new file mode 100644
index 000000000..d8efc9705
--- /dev/null
+++ b/source/reduce/reduction_util.h
@@ -0,0 +1,33 @@
+// Copyright (c) 2018 Google LLC
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef SOURCE_REDUCE_REDUCTION_UTIL_H_
+#define SOURCE_REDUCE_REDUCTION_UTIL_H_
+
+#include "spirv-tools/libspirv.hpp"
+
+#include "source/opt/ir_context.h"
+#include "source/reduce/reduction_opportunity.h"
+
+namespace spvtools {
+namespace reduce {
+
+// Returns an OpUndef id from the global value list that is of the given type,
+// adding one if it does not exist.
+uint32_t FindOrCreateGlobalUndef(opt::IRContext* context, uint32_t type_id);
+
+}  // namespace reduce
+}  // namespace spvtools
+
+#endif  // SOURCE_REDUCE_REDUCTION_UTIL_H_
diff --git a/source/reduce/remove_instruction_reduction_opportunity.h b/source/reduce/remove_instruction_reduction_opportunity.h
index 471ff15e3..e9f442e3f 100644
--- a/source/reduce/remove_instruction_reduction_opportunity.h
+++ b/source/reduce/remove_instruction_reduction_opportunity.h
@@ -23,18 +23,17 @@ namespace reduce {
 
 using namespace opt;
 
-// Captures the opportunity to remove an instruction from the SPIR-V module.
+// An opportunity to remove an instruction from the SPIR-V module.
 class RemoveInstructionReductionOpportunity : public ReductionOpportunity {
  public:
   // Constructs the opportunity to remove |inst|.
   explicit RemoveInstructionReductionOpportunity(Instruction* inst)
       : inst_(inst) {}
 
-  // This kind of opportunity can be unconditionally applied.
+  // Always returns true, as this opportunity can always be applied.
   bool PreconditionHolds() override;
 
  protected:
-  // Remove the instruction.
   void Apply() override;
 
  private:
diff --git a/source/reduce/remove_opname_instruction_reduction_pass.h b/source/reduce/remove_opname_instruction_reduction_pass.h
index d20b6e182..2990a49cc 100644
--- a/source/reduce/remove_opname_instruction_reduction_pass.h
+++ b/source/reduce/remove_opname_instruction_reduction_pass.h
@@ -21,8 +21,9 @@ namespace spvtools {
 namespace reduce {
 
 // A reduction pass for removing OpName instructions.  As well as making the
-// module smaller, removing an OpName instruction may create opportunities to
-// remove the instruction that create the id to which the OpName applies.
+// module smaller, removing an OpName instruction may create opportunities
+// for subsequently removing the instructions that create the ids to which the
+// OpName applies.
 class RemoveOpNameInstructionReductionPass : public ReductionPass {
  public:
   // Creates the reduction pass in the context of the given target environment
@@ -32,12 +33,9 @@ class RemoveOpNameInstructionReductionPass : public ReductionPass {
 
   ~RemoveOpNameInstructionReductionPass() override = default;
 
-  // The name of this pass.
   std::string GetName() const final;
 
  protected:
-  // Finds all opportunities for removing opName instructions in the
-  // given module.
   std::vector<std::unique_ptr<ReductionOpportunity>> GetAvailableOpportunities(
       opt::IRContext* context) const final;
 
diff --git a/source/reduce/remove_unreferenced_instruction_reduction_pass.h b/source/reduce/remove_unreferenced_instruction_reduction_pass.h
index 27c3fc2d4..44a0d55e9 100644
--- a/source/reduce/remove_unreferenced_instruction_reduction_pass.h
+++ b/source/reduce/remove_unreferenced_instruction_reduction_pass.h
@@ -22,7 +22,7 @@ namespace reduce {
 
 // A reduction pass for removing non-control-flow instructions in blocks in
 // cases where the instruction's id is not referenced.  As well as making the
-// module smaller, removing an instruction that referenced particular ids may
+// module smaller, removing an instruction that references particular ids may
 // create opportunities for subsequently removing the instructions that
 // generated those ids.
 class RemoveUnreferencedInstructionReductionPass : public ReductionPass {
@@ -35,12 +35,9 @@ class RemoveUnreferencedInstructionReductionPass : public ReductionPass {
 
   ~RemoveUnreferencedInstructionReductionPass() override = default;
 
-  // The name of this pass.
   std::string GetName() const final;
 
  protected:
-  // Finds all opportunities for removing unreferenced instructions in the
-  // given module.
   std::vector<std::unique_ptr<ReductionOpportunity>> GetAvailableOpportunities(
       opt::IRContext* context) const final;
 
diff --git a/source/reduce/structured_loop_to_selection_reduction_opportunity.cpp b/source/reduce/structured_loop_to_selection_reduction_opportunity.cpp
index 679cfc1a6..bf0e085ad 100644
--- a/source/reduce/structured_loop_to_selection_reduction_opportunity.cpp
+++ b/source/reduce/structured_loop_to_selection_reduction_opportunity.cpp
@@ -12,9 +12,11 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "structured_loop_to_selection_reduction_opportunity.h"
+#include "source/reduce/structured_loop_to_selection_reduction_opportunity.h"
+
 #include "source/opt/aggressive_dead_code_elim_pass.h"
 #include "source/opt/ir_context.h"
+#include "source/reduce/reduction_util.h"
 
 namespace spvtools {
 namespace reduce {
@@ -191,7 +193,7 @@ void StructuredLoopToSelectionReductionOpportunity::
   to_block->ForEachPhiInst([this, &from_id](Instruction* phi_inst) {
     // Add to the phi operand an (undef, from_id) pair to reflect the added
     // edge.
-    auto undef_id = FindOrCreateGlobalUndef(phi_inst->type_id());
+    auto undef_id = FindOrCreateGlobalUndef(context_, phi_inst->type_id());
     phi_inst->AddOperand(Operand(SPV_OPERAND_TYPE_ID, {undef_id}));
     phi_inst->AddOperand(Operand(SPV_OPERAND_TYPE_ID, {from_id}));
   });
@@ -273,7 +275,8 @@ void StructuredLoopToSelectionReductionOpportunity::FixNonDominatedIdUses() {
                 break;
             }
           } else {
-            use->SetOperand(index, {FindOrCreateGlobalUndef(def.type_id())});
+            use->SetOperand(index,
+                            {FindOrCreateGlobalUndef(context_, def.type_id())});
           }
         }
       });
@@ -296,26 +299,6 @@ bool StructuredLoopToSelectionReductionOpportunity::
       ->Dominates(def, use);
 }
 
-uint32_t StructuredLoopToSelectionReductionOpportunity::FindOrCreateGlobalUndef(
-    uint32_t type_id) {
-  for (auto& inst : context_->module()->types_values()) {
-    if (inst.opcode() != SpvOpUndef) {
-      continue;
-    }
-    if (inst.type_id() == type_id) {
-      return inst.result_id();
-    }
-  }
-  // TODO(2182): this is adapted from MemPass::Type2Undef.  In due course it
-  // would be good to factor out this duplication.
-  const uint32_t undef_id = context_->TakeNextId();
-  std::unique_ptr<Instruction> undef_inst(
-      new Instruction(context_, SpvOpUndef, type_id, undef_id, {}));
-  assert(undef_id == undef_inst->result_id());
-  context_->module()->AddGlobalValue(std::move(undef_inst));
-  return undef_id;
-}
-
 uint32_t
 StructuredLoopToSelectionReductionOpportunity::FindOrCreateGlobalVariable(
     uint32_t pointer_type_id) {
diff --git a/source/reduce/structured_loop_to_selection_reduction_opportunity.h b/source/reduce/structured_loop_to_selection_reduction_opportunity.h
index b13901683..71b0f0eb4 100644
--- a/source/reduce/structured_loop_to_selection_reduction_opportunity.h
+++ b/source/reduce/structured_loop_to_selection_reduction_opportunity.h
@@ -15,17 +15,17 @@
 #ifndef SOURCE_REDUCE_CUT_LOOP_REDUCTION_OPPORTUNITY_H_
 #define SOURCE_REDUCE_CUT_LOOP_REDUCTION_OPPORTUNITY_H_
 
-#include <source/opt/def_use_manager.h>
-#include "reduction_opportunity.h"
+#include "source/opt/def_use_manager.h"
 #include "source/opt/dominator_analysis.h"
 #include "source/opt/function.h"
+#include "source/reduce/reduction_opportunity.h"
 
 namespace spvtools {
 namespace reduce {
 
 using namespace opt;
 
-// Captures an opportunity to replace a structured loop with a selection.
+// An opportunity to replace a structured loop with a selection.
 class StructuredLoopToSelectionReductionOpportunity
     : public ReductionOpportunity {
  public:
@@ -38,13 +38,12 @@ class StructuredLoopToSelectionReductionOpportunity
         loop_construct_header_(loop_construct_header),
         enclosing_function_(enclosing_function) {}
 
-  // We require the loop header to be reachable.  A structured loop might
+  // Returns true if the loop header is reachable.  A structured loop might
   // become unreachable as a result of turning another structured loop into
   // a selection.
   bool PreconditionHolds() override;
 
  protected:
-  // Perform the structured loop to selection transformation.
   void Apply() override;
 
  private:
@@ -92,14 +91,6 @@ class StructuredLoopToSelectionReductionOpportunity
                                           uint32_t use_index,
                                           BasicBlock& def_block);
 
-  // Checks whether the global value list has an OpUndef of the given type,
-  // adding one if not, and returns the id of such an OpUndef.
-  //
-  // TODO(2184): This will likely be used by other reduction passes, so should
-  // be factored out in due course.  Parts of the spirv-opt framework provide
-  // similar functionality, so there may be a case for further refactoring.
-  uint32_t FindOrCreateGlobalUndef(uint32_t type_id);
-
   // Checks whether the global value list has an OpVariable of the given pointer
   // type, adding one if not, and returns the id of such an OpVariable.
   //
diff --git a/source/reduce/structured_loop_to_selection_reduction_pass.h b/source/reduce/structured_loop_to_selection_reduction_pass.h
index 9c4d4caee..a1f88bc54 100644
--- a/source/reduce/structured_loop_to_selection_reduction_pass.h
+++ b/source/reduce/structured_loop_to_selection_reduction_pass.h
@@ -46,12 +46,9 @@ class StructuredLoopToSelectionReductionPass : public ReductionPass {
 
   ~StructuredLoopToSelectionReductionPass() override = default;
 
-  // The name of this pass.
   std::string GetName() const final;
 
  protected:
-  // Finds all opportunities for transforming a structured loop to a selection
-  // in the given module.
   std::vector<std::unique_ptr<ReductionOpportunity>> GetAvailableOpportunities(
       opt::IRContext* context) const final;
 
diff --git a/test/reduce/CMakeLists.txt b/test/reduce/CMakeLists.txt
index cdd27b9e1..b35cdb260 100644
--- a/test/reduce/CMakeLists.txt
+++ b/test/reduce/CMakeLists.txt
@@ -14,6 +14,7 @@
 
 add_spvtools_unittest(TARGET reduce
         SRCS operand_to_constant_reduction_pass_test.cpp
+        operand_to_undef_reduction_pass_test.cpp
         operand_to_dominating_id_reduction_pass_test.cpp
         reduce_test_util.cpp
         reduce_test_util.h
diff --git a/test/reduce/operand_to_undef_reduction_pass_test.cpp b/test/reduce/operand_to_undef_reduction_pass_test.cpp
new file mode 100644
index 000000000..71bf96cf4
--- /dev/null
+++ b/test/reduce/operand_to_undef_reduction_pass_test.cpp
@@ -0,0 +1,226 @@
+// Copyright (c) 2018 Google LLC
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "source/reduce/operand_to_undef_reduction_pass.h"
+#include "source/opt/build_module.h"
+#include "test/reduce/reduce_test_util.h"
+
+namespace spvtools {
+namespace reduce {
+namespace {
+
+TEST(OperandToUndefReductionPassTest, BasicCheck) {
+  // The following shader has 10 opportunities for replacing with undef.
+
+  //    #version 310 es
+  //
+  //    precision highp float;
+  //
+  //    layout(location=0) out vec4 _GLF_color;
+  //
+  //    layout(set = 0, binding = 0) uniform buf0 {
+  //        vec2 uniform1;
+  //    };
+  //
+  //    void main()
+  //    {
+  //        _GLF_color =
+  //            vec4(                          // opportunity
+  //                uniform1.x / 2.0,          // opportunity x2 (2.0 is const)
+  //                uniform1.y / uniform1.x,   // opportunity x3
+  //                uniform1.x + uniform1.x,   // opportunity x3
+  //                uniform1.y);               // opportunity
+  //    }
+
+  std::string original = R"(
+               OpCapability Shader
+          %1 = OpExtInstImport "GLSL.std.450"
+               OpMemoryModel Logical GLSL450
+               OpEntryPoint Fragment %4 "main" %9
+               OpExecutionMode %4 OriginUpperLeft
+               OpSource ESSL 310
+               OpName %4 "main"
+               OpName %9 "_GLF_color"
+               OpName %11 "buf0"
+               OpMemberName %11 0 "uniform1"
+               OpName %13 ""
+               OpDecorate %9 Location 0
+               OpMemberDecorate %11 0 Offset 0
+               OpDecorate %11 Block
+               OpDecorate %13 DescriptorSet 0
+               OpDecorate %13 Binding 0
+          %2 = OpTypeVoid
+          %3 = OpTypeFunction %2
+          %6 = OpTypeFloat 32
+          %7 = OpTypeVector %6 4
+          %8 = OpTypePointer Output %7
+          %9 = OpVariable %8 Output
+         %10 = OpTypeVector %6 2
+         %11 = OpTypeStruct %10
+         %12 = OpTypePointer Uniform %11
+         %13 = OpVariable %12 Uniform
+         %14 = OpTypeInt 32 1
+         %15 = OpConstant %14 0
+         %16 = OpTypeInt 32 0
+         %17 = OpConstant %16 0
+         %18 = OpTypePointer Uniform %6
+         %21 = OpConstant %6 2
+         %23 = OpConstant %16 1
+          %4 = OpFunction %2 None %3
+          %5 = OpLabel
+         %19 = OpAccessChain %18 %13 %15 %17
+         %20 = OpLoad %6 %19
+         %22 = OpFDiv %6 %20 %21                         ; opportunity %20 (%21 is const)
+         %24 = OpAccessChain %18 %13 %15 %23
+         %25 = OpLoad %6 %24
+         %26 = OpAccessChain %18 %13 %15 %17
+         %27 = OpLoad %6 %26
+         %28 = OpFDiv %6 %25 %27                         ; opportunity %25 %27
+         %29 = OpAccessChain %18 %13 %15 %17
+         %30 = OpLoad %6 %29
+         %31 = OpAccessChain %18 %13 %15 %17
+         %32 = OpLoad %6 %31
+         %33 = OpFAdd %6 %30 %32                         ; opportunity %30 %32
+         %34 = OpAccessChain %18 %13 %15 %23
+         %35 = OpLoad %6 %34
+         %36 = OpCompositeConstruct %7 %22 %28 %33 %35   ; opportunity %22 %28 %33 %35
+               OpStore %9 %36                            ; opportunity %36
+               OpReturn
+               OpFunctionEnd
+  )";
+
+  // This is the same as original, except where noted.
+  std::string expected = R"(
+               OpCapability Shader
+          %1 = OpExtInstImport "GLSL.std.450"
+               OpMemoryModel Logical GLSL450
+               OpEntryPoint Fragment %4 "main" %9
+               OpExecutionMode %4 OriginUpperLeft
+               OpSource ESSL 310
+               OpName %4 "main"
+               OpName %9 "_GLF_color"
+               OpName %11 "buf0"
+               OpMemberName %11 0 "uniform1"
+               OpName %13 ""
+               OpDecorate %9 Location 0
+               OpMemberDecorate %11 0 Offset 0
+               OpDecorate %11 Block
+               OpDecorate %13 DescriptorSet 0
+               OpDecorate %13 Binding 0
+          %2 = OpTypeVoid
+          %3 = OpTypeFunction %2
+          %6 = OpTypeFloat 32
+          %7 = OpTypeVector %6 4
+          %8 = OpTypePointer Output %7
+          %9 = OpVariable %8 Output
+         %10 = OpTypeVector %6 2
+         %11 = OpTypeStruct %10
+         %12 = OpTypePointer Uniform %11
+         %13 = OpVariable %12 Uniform
+         %14 = OpTypeInt 32 1
+         %15 = OpConstant %14 0
+         %16 = OpTypeInt 32 0
+         %17 = OpConstant %16 0
+         %18 = OpTypePointer Uniform %6
+         %21 = OpConstant %6 2
+         %23 = OpConstant %16 1
+         %37 = OpUndef %6                            ; Added undef float as %37
+          %4 = OpFunction %2 None %3
+          %5 = OpLabel
+         %19 = OpAccessChain %18 %13 %15 %17
+         %20 = OpLoad %6 %19
+         %22 = OpFDiv %6 %37 %21                     ; Replaced with %37
+         %24 = OpAccessChain %18 %13 %15 %23
+         %25 = OpLoad %6 %24
+         %26 = OpAccessChain %18 %13 %15 %17
+         %27 = OpLoad %6 %26
+         %28 = OpFDiv %6 %37 %37                     ; Replaced with %37 twice
+         %29 = OpAccessChain %18 %13 %15 %17
+         %30 = OpLoad %6 %29
+         %31 = OpAccessChain %18 %13 %15 %17
+         %32 = OpLoad %6 %31
+         %33 = OpFAdd %6 %30 %32
+         %34 = OpAccessChain %18 %13 %15 %23
+         %35 = OpLoad %6 %34
+         %36 = OpCompositeConstruct %7 %22 %28 %33 %35
+               OpStore %9 %36
+               OpReturn
+               OpFunctionEnd
+  )";
+
+  const auto env = SPV_ENV_UNIVERSAL_1_3;
+  const auto consumer = nullptr;
+  const auto context =
+      BuildModule(env, consumer, original, kReduceAssembleOption);
+  const auto pass = TestSubclass<OperandToUndefReductionPass>(env);
+  const auto ops = pass.WrapGetAvailableOpportunities(context.get());
+
+  ASSERT_EQ(10, ops.size());
+
+  // Apply first three opportunities.
+  ASSERT_TRUE(ops[0]->PreconditionHolds());
+  ops[0]->TryToApply();
+  ASSERT_TRUE(ops[1]->PreconditionHolds());
+  ops[1]->TryToApply();
+  ASSERT_TRUE(ops[2]->PreconditionHolds());
+  ops[2]->TryToApply();
+
+  CheckEqual(env, expected, context.get());
+}
+
+TEST(OperandToUndefReductionPassTest, WithCalledFunction) {
+  // The following shader has no opportunities.
+  // Most importantly, the noted function operand is not changed.
+
+  std::string shader = R"(
+               OpCapability Shader
+          %1 = OpExtInstImport "GLSL.std.450"
+               OpMemoryModel Logical GLSL450
+               OpEntryPoint Fragment %4 "main" %10 %12
+               OpExecutionMode %4 OriginUpperLeft
+               OpSource ESSL 310
+          %2 = OpTypeVoid
+          %3 = OpTypeFunction %2
+          %6 = OpTypeFloat 32
+          %7 = OpTypeVector %6 4
+          %8 = OpTypeFunction %7
+          %9 = OpTypePointer Output %7
+         %10 = OpVariable %9 Output
+         %11 = OpTypePointer Input %7
+         %12 = OpVariable %11 Input
+         %13 = OpConstant %6 0
+         %14 = OpConstantComposite %7 %13 %13 %13 %13
+          %4 = OpFunction %2 None %3
+          %5 = OpLabel
+         %15 = OpFunctionCall %7 %16            ; do not replace %16 with undef
+               OpReturn
+               OpFunctionEnd
+         %16 = OpFunction %7 None %8
+         %17 = OpLabel
+               OpReturnValue %14
+               OpFunctionEnd
+  )";
+
+  const auto env = SPV_ENV_UNIVERSAL_1_3;
+  const auto consumer = nullptr;
+  const auto context =
+      BuildModule(env, consumer, shader, kReduceAssembleOption);
+  const auto pass = TestSubclass<OperandToUndefReductionPass>(env);
+  const auto ops = pass.WrapGetAvailableOpportunities(context.get());
+  ASSERT_EQ(0, ops.size());
+}
+
+}  // namespace
+}  // namespace reduce
+}  // namespace spvtools
diff --git a/tools/reduce/reduce.cpp b/tools/reduce/reduce.cpp
index 390724a6d..65325f745 100644
--- a/tools/reduce/reduce.cpp
+++ b/tools/reduce/reduce.cpp
@@ -22,6 +22,7 @@
 #include "source/opt/log.h"
 #include "source/reduce/operand_to_const_reduction_pass.h"
 #include "source/reduce/operand_to_dominating_id_reduction_pass.h"
+#include "source/reduce/operand_to_undef_reduction_pass.h"
 #include "source/reduce/reducer.h"
 #include "source/reduce/remove_opname_instruction_reduction_pass.h"
 #include "source/reduce/remove_unreferenced_instruction_reduction_pass.h"
@@ -207,6 +208,8 @@ int main(int argc, const char** argv) {
 
   reducer.AddReductionPass(
       spvtools::MakeUnique<RemoveOpNameInstructionReductionPass>(target_env));
+  reducer.AddReductionPass(
+      spvtools::MakeUnique<OperandToUndefReductionPass>(target_env));
   reducer.AddReductionPass(
       spvtools::MakeUnique<OperandToConstReductionPass>(target_env));
   reducer.AddReductionPass(