diff --git a/src/core/SkBBoxHierarchy.h b/src/core/SkBBoxHierarchy.h
index 36047b9706..b42f708bc7 100644
--- a/src/core/SkBBoxHierarchy.h
+++ b/src/core/SkBBoxHierarchy.h
@@ -59,7 +59,7 @@ public:
     /**
      * Populate 'results' with data pointers corresponding to bounding boxes that intersect 'query'
      */
-    virtual void search(const SkIRect& query, SkTDArray<void*>* results) = 0;
+    virtual void search(const SkIRect& query, SkTDArray<void*>* results) const = 0;
 
     virtual void clear() = 0;
 
diff --git a/src/core/SkQuadTree.cpp b/src/core/SkQuadTree.cpp
index a11613d08b..1fc3cd0192 100644
--- a/src/core/SkQuadTree.cpp
+++ b/src/core/SkQuadTree.cpp
@@ -168,7 +168,7 @@ void SkQuadTree::insert(void* data, const SkIRect& bounds, bool) {
     }
 }
 
-void SkQuadTree::search(const SkIRect& query, SkTDArray<void*>* results) {
+void SkQuadTree::search(const SkIRect& query, SkTDArray<void*>* results) const {
     SkASSERT(NULL != fRoot);
     SkASSERT(NULL != results);
     if (SkIRect::Intersects(fRootBounds, query)) {
diff --git a/src/core/SkQuadTree.h b/src/core/SkQuadTree.h
index bf1bc8ebba..faa33fca45 100644
--- a/src/core/SkQuadTree.h
+++ b/src/core/SkQuadTree.h
@@ -54,7 +54,7 @@ public:
     /**
      * Given a query rectangle, populates the passed-in array with the elements it intersects
      */
-    virtual void search(const SkIRect& query, SkTDArray<void*>* results) SK_OVERRIDE;
+    virtual void search(const SkIRect& query, SkTDArray<void*>* results) const SK_OVERRIDE;
 
     virtual void clear() SK_OVERRIDE;
 
diff --git a/src/core/SkRTree.cpp b/src/core/SkRTree.cpp
index fe08437da3..3985fb1285 100644
--- a/src/core/SkRTree.cpp
+++ b/src/core/SkRTree.cpp
@@ -102,11 +102,9 @@ void SkRTree::flushDeferredInserts() {
     this->validate();
 }
 
-void SkRTree::search(const SkIRect& query, SkTDArray<void*>* results) {
+void SkRTree::search(const SkIRect& query, SkTDArray<void*>* results) const {
     this->validate();
-    if (0 != fDeferredInserts.count()) {
-        this->flushDeferredInserts();
-    }
+    SkASSERT(0 == fDeferredInserts.count());  // If this fails, you should have flushed.
     if (!this->isEmpty() && SkIRect::IntersectsNoEmptyCheck(fRoot.fBounds, query)) {
         this->search(fRoot.fChild.subtree, query, results);
     }
@@ -399,7 +397,7 @@ SkRTree::Branch SkRTree::bulkLoad(SkTDArray<Branch>* branches, int level) {
     }
 }
 
-void SkRTree::validate() {
+void SkRTree::validate() const {
 #ifdef SK_DEBUG
     if (this->isEmpty()) {
         return;
@@ -408,7 +406,7 @@ void SkRTree::validate() {
 #endif
 }
 
-int SkRTree::validateSubtree(Node* root, SkIRect bounds, bool isRoot) {
+int SkRTree::validateSubtree(Node* root, SkIRect bounds, bool isRoot) const {
     // make sure the pointer is pointing to a valid place
     SkASSERT(fNodes.contains(static_cast<void*>(root)));
 
diff --git a/src/core/SkRTree.h b/src/core/SkRTree.h
index d21b5f8d37..6487b324ef 100644
--- a/src/core/SkRTree.h
+++ b/src/core/SkRTree.h
@@ -77,7 +77,7 @@ public:
     /**
      * Given a query rectangle, populates the passed-in array with the elements it intersects
      */
-    virtual void search(const SkIRect& query, SkTDArray<void*>* results) SK_OVERRIDE;
+    virtual void search(const SkIRect& query, SkTDArray<void*>* results) const SK_OVERRIDE;
 
     virtual void clear() SK_OVERRIDE;
     bool isEmpty() const { return 0 == fCount; }
@@ -177,8 +177,8 @@ private:
      */
     Branch bulkLoad(SkTDArray<Branch>* branches, int level = 0);
 
-    void validate();
-    int validateSubtree(Node* root, SkIRect bounds, bool isRoot = false);
+    void validate() const;
+    int validateSubtree(Node* root, SkIRect bounds, bool isRoot = false) const;
 
     const int fMinChildren;
     const int fMaxChildren;
diff --git a/src/core/SkTileGrid.cpp b/src/core/SkTileGrid.cpp
index 35f85d26c9..c86e78928c 100644
--- a/src/core/SkTileGrid.cpp
+++ b/src/core/SkTileGrid.cpp
@@ -33,6 +33,10 @@ int SkTileGrid::tileCount(int x, int y) {
     return this->tile(x, y).count();
 }
 
+const SkTDArray<void *>& SkTileGrid::tile(int x, int y) const {
+    return fTileData[y * fXTileCount + x];
+}
+
 SkTDArray<void *>& SkTileGrid::tile(int x, int y) {
     return fTileData[y * fXTileCount + x];
 }
@@ -65,7 +69,7 @@ void SkTileGrid::insert(void* data, const SkIRect& bounds, bool) {
     fInsertionCount++;
 }
 
-void SkTileGrid::search(const SkIRect& query, SkTDArray<void*>* results) {
+void SkTileGrid::search(const SkIRect& query, SkTDArray<void*>* results) const {
     SkIRect adjustedQuery = query;
     // The inset is to counteract the outset that was applied in 'insert'
     // The outset/inset is to optimize for lookups of size
@@ -96,7 +100,7 @@ void SkTileGrid::search(const SkIRect& query, SkTDArray<void*>* results) {
         results->reset();
         SkAutoSTArray<kStackAllocationTileCount, int> curPositions(queryTileCount);
         SkAutoSTArray<kStackAllocationTileCount, SkTDArray<void *>*> storage(queryTileCount);
-        SkTDArray<void *>** tileRange = storage.get();
+        const SkTDArray<void *>** tileRange = const_cast<const SkTDArray<void*>**>(storage.get());
         int tile = 0;
         for (int x = tileStartX; x < tileEndX; ++x) {
             for (int y = tileStartY; y < tileEndY; ++y) {
diff --git a/src/core/SkTileGrid.h b/src/core/SkTileGrid.h
index 0ec5c2c393..ea473fb6d0 100644
--- a/src/core/SkTileGrid.h
+++ b/src/core/SkTileGrid.h
@@ -33,7 +33,9 @@ public:
         kStackAllocationTileCount = 1024
     };
 
-    typedef void* (*SkTileGridNextDatumFunctionPtr)(SkTDArray<void*>** tileData, SkAutoSTArray<kStackAllocationTileCount, int>& tileIndices);
+    typedef void* (*SkTileGridNextDatumFunctionPtr)(
+            const SkTDArray<void*>** tileData,
+            SkAutoSTArray<kStackAllocationTileCount, int>& tileIndices);
 
     SkTileGrid(int xTileCount, int yTileCount, const SkTileGridFactory::TileGridInfo& info,
         SkTileGridNextDatumFunctionPtr nextDatumFunction);
@@ -54,7 +56,7 @@ public:
      * Populate 'results' with data pointers corresponding to bounding boxes that intersect 'query'
      * The query argument is expected to be an exact match to a tile of the grid
      */
-    virtual void search(const SkIRect& query, SkTDArray<void*>* results) SK_OVERRIDE;
+    virtual void search(const SkIRect& query, SkTDArray<void*>* results) const SK_OVERRIDE;
 
     virtual void clear() SK_OVERRIDE;
 
@@ -75,6 +77,7 @@ public:
     int tileCount(int x, int y);  // For testing only.
 
 private:
+    const SkTDArray<void*>& tile(int x, int y) const;
     SkTDArray<void*>& tile(int x, int y);
 
     int fXTileCount, fYTileCount, fTileCount;
@@ -103,7 +106,8 @@ private:
  *     such that 'a < b' is true if 'a' was inserted into the tile grid before 'b'.
  */
 template <typename T>
-void* SkTileGridNextDatum(SkTDArray<void*>** tileData, SkAutoSTArray<SkTileGrid::kStackAllocationTileCount, int>& tileIndices) {
+void* SkTileGridNextDatum(const SkTDArray<void*>** tileData,
+                          SkAutoSTArray<SkTileGrid::kStackAllocationTileCount, int>& tileIndices) {
     T* minVal = NULL;
     int tileCount = tileIndices.count();
     int minIndex = tileCount;