diff --git a/src/codegen/compiler.cc b/src/codegen/compiler.cc
index c39cddb733..aa15af30db 100644
--- a/src/codegen/compiler.cc
+++ b/src/codegen/compiler.cc
@@ -1596,7 +1596,7 @@ bool Compiler::FinalizeBackgroundCompileTask(
   Handle<Script> script(Script::cast(shared_info->script()), isolate);
   // TODO(leszeks): We can probably remove this, the parse_info flags should
   // already match the script's.
-  parse_info->SetFlagsFromScript(isolate, *script);
+  parse_info->SetFlagsForFunctionFromScript(*script);
 
   task->parser()->UpdateStatistics(isolate, script);
   task->parser()->HandleSourceURLComments(isolate, script);
diff --git a/src/parsing/parse-info.cc b/src/parsing/parse-info.cc
index de2298dad0..ff454462ca 100644
--- a/src/parsing/parse-info.cc
+++ b/src/parsing/parse-info.cc
@@ -104,7 +104,11 @@ ParseInfo::ParseInfo(Isolate* isolate, SharedFunctionInfo shared)
   SetFunctionInfo(&shared);
 
   Script script = Script::cast(shared.script());
-  SetFlagsFromScript(isolate, script);
+  SetFlagsForFunctionFromScript(script);
+  if (shared.is_wrapped()) {
+    DCHECK(script.is_wrapped());
+    set_wrapped_arguments(handle(script.wrapped_arguments(), isolate));
+  }
 
   if (shared.HasOuterScopeInfo()) {
     set_outer_scope_info(handle(shared.GetOuterScopeInfo(), isolate));
@@ -238,19 +242,20 @@ void ParseInfo::set_character_stream(
 template <typename LocalIsolate>
 void ParseInfo::SetFlagsForToplevelCompileFromScript(
     LocalIsolate* isolate, Script script, bool is_collecting_type_profile) {
-  SetFlagsFromScript(isolate, script);
+  SetFlagsForFunctionFromScript(script);
   set_allow_lazy_parsing();
   set_toplevel();
   set_collect_type_profile(is_collecting_type_profile &&
                            script.IsUserJavaScript());
   set_repl_mode(script.is_repl_mode());
+
   if (script.is_wrapped()) {
     set_function_syntax_kind(FunctionSyntaxKind::kWrapped);
+    set_wrapped_arguments(handle(script.wrapped_arguments(), isolate));
   }
 }
 
-template <typename LocalIsolate>
-void ParseInfo::SetFlagsFromScript(LocalIsolate* isolate, Script script) {
+void ParseInfo::SetFlagsForFunctionFromScript(Script script) {
   DCHECK(script_id_ == -1 || script_id_ == script.id());
   script_id_ = script.id();
 
@@ -261,16 +266,6 @@ void ParseInfo::SetFlagsFromScript(LocalIsolate* isolate, Script script) {
   if (block_coverage_enabled() && script.IsUserJavaScript()) {
     AllocateSourceRangeMap();
   }
-
-  if (script.is_wrapped()) {
-    // This should only ever happen on the main thread. Convert this templated
-    // handle into a real Handle via Handle to avoid having to
-    // use template specialization for this.
-    DCHECK((std::is_same<Isolate, v8::internal::Isolate>::value));
-    Handle<FixedArray> wrapped_arguments_handle =
-        handle(script.wrapped_arguments(), isolate);
-    set_wrapped_arguments(wrapped_arguments_handle);
-  }
 }
 
 void ParseInfo::ParallelTasks::Enqueue(ParseInfo* outer_parse_info,
diff --git a/src/parsing/parse-info.h b/src/parsing/parse-info.h
index 49b195798b..dc9e9751bb 100644
--- a/src/parsing/parse-info.h
+++ b/src/parsing/parse-info.h
@@ -264,8 +264,7 @@ class V8_EXPORT_PRIVATE ParseInfo {
 
   ParallelTasks* parallel_tasks() { return parallel_tasks_.get(); }
 
-  template <typename LocalIsolate>
-  void SetFlagsFromScript(LocalIsolate* isolate, Script script);
+  void SetFlagsForFunctionFromScript(Script script);
 
   //--------------------------------------------------------------------------
   // TODO(titzer): these should not be part of ParseInfo.