Index: llvm/lib/Transforms/Utils/CloneFunction.cpp
===================================================================
--- llvm/lib/Transforms/Utils/CloneFunction.cpp
+++ llvm/lib/Transforms/Utils/CloneFunction.cpp
@@ -105,18 +105,25 @@
   NewFunc->copyAttributesFrom(OldFunc);
   NewFunc->setAttributes(NewAttrs);
 
+  const RemapFlags FuncGlobalRefFlags =
+      ModuleLevelChanges ? RF_None : RF_NoModuleLevelChanges;
+
   // Fix up the personality function that got copied over.
   if (OldFunc->hasPersonalityFn())
-    NewFunc->setPersonalityFn(
-        MapValue(OldFunc->getPersonalityFn(), VMap,
-                 ModuleLevelChanges ? RF_None : RF_NoModuleLevelChanges,
-                 TypeMapper, Materializer));
+    NewFunc->setPersonalityFn(MapValue(OldFunc->getPersonalityFn(), VMap,
+                                       FuncGlobalRefFlags, TypeMapper,
+                                       Materializer));
 
   if (OldFunc->hasPrefixData()) {
-    NewFunc->setPrefixData(
-        MapValue(OldFunc->getPrefixData(), VMap,
-                 ModuleLevelChanges ? RF_None : RF_NoModuleLevelChanges,
-                 TypeMapper, Materializer));
+    NewFunc->setPrefixData(MapValue(OldFunc->getPrefixData(), VMap,
+                                    FuncGlobalRefFlags, TypeMapper,
+                                    Materializer));
+  }
+
+  if (OldFunc->hasPrologueData()) {
+    NewFunc->setPrologueData(MapValue(OldFunc->getPrologueData(), VMap,
+                                      FuncGlobalRefFlags, TypeMapper,
+                                      Materializer));
   }
 
   SmallVector<AttributeSet, 4> NewArgAttrs(NewFunc->arg_size());
Index: llvm/test/tools/llvm-reduce/reduce-prolog-data.ll
===================================================================
--- /dev/null
+++ llvm/test/tools/llvm-reduce/reduce-prolog-data.ll
@@ -0,0 +1,47 @@
+; RUN: llvm-reduce --abort-on-invalid-reduction --delta-passes=function-data --test FileCheck --test-arg --check-prefix=CHECK --test-arg %s --test-arg --input-file %s -o %t
+; RUN: FileCheck -check-prefixes=CHECK,RESULT %s < %t
+
+@gv = linkonce_odr global i32 1
+
+; CHECK: define void @drop_prologue_const_array()
+define void @drop_prologue_const_array() prologue [2 x i32] [i32 1, i32 2] {
+  ret void
+}
+
+; CHECK: define void @keep_prologue_const_array() prologue i32 1 {
+define void @keep_prologue_const_array() prologue i32 1 {
+  ret void
+}
+
+; CHECK: define void @drop_prologue_ptr_global()
+define void @drop_prologue_ptr_global() prologue ptr @gv {
+  ret void
+}
+
+; CHECK: define void @keep_prologue_ptr_global() prologue ptr @gv {
+define void @keep_prologue_ptr_global() prologue ptr @gv {
+  ret void
+}
+
+; Make sure there's no invalid reduction if the prologue data is really
+; accessed
+; CHECK: define i32 @drop_uses_prologue_const_array()
+define i32 @drop_uses_prologue_const_array() prologue [2 x i32] [i32 1, i32 2] {
+  %gep = getelementptr inbounds i32, ptr @drop_uses_prologue_const_array, i32 -1
+  %load = load i32, ptr %gep
+  ret i32 %load
+}
+
+; CHECK: define ptr @drop_uses_prologue_gv(
+define ptr @drop_uses_prologue_gv() prologue ptr @gv {
+  %gep = getelementptr inbounds i32, ptr @drop_uses_prologue_gv, i32 -1
+  %load = load ptr, ptr %gep
+  ret ptr %load
+}
+
+
+; RESULT: declare void @declaration_prologue_const_array(){{$}}
+declare void @declaration_prologue_const_array() prologue [2 x i32] [i32 1, i32 2]
+
+; RESULT: void @declaration_prologue_ptr_gv(){{$}}
+declare void @declaration_prologue_ptr_gv() prologue ptr @gv
Index: llvm/tools/llvm-reduce/deltas/ReduceFunctionBodies.cpp
===================================================================
--- llvm/tools/llvm-reduce/deltas/ReduceFunctionBodies.cpp
+++ llvm/tools/llvm-reduce/deltas/ReduceFunctionBodies.cpp
@@ -51,7 +51,8 @@
     if (F.hasPrefixData() && !O.shouldKeep())
       F.setPrefixData(nullptr);
 
-    // TODO: Handle prologue data
+    if (F.hasPrologueData() && !O.shouldKeep())
+      F.setPrologueData(nullptr);
   }
 }