Index: llvm/lib/Transforms/IPO/FunctionSpecialization.cpp
===================================================================
--- llvm/lib/Transforms/IPO/FunctionSpecialization.cpp
+++ llvm/lib/Transforms/IPO/FunctionSpecialization.cpp
@@ -406,11 +406,15 @@
       llvm::sort(Worklist,
                  [] (ArgInfo &L, ArgInfo &R) { return L.Gain > R.Gain; });
 
-      // TODO: truncate the worklist to 'MaxConstantsThreshold' candidates if
+      // Truncate the worklist to 'MaxConstantsThreshold' candidates if
       // necessary.
       if (Worklist.size() > MaxConstantsThreshold) {
-        Worklist.clear();
-        continue;
+        LLVM_DEBUG(dbgs() << "FnSpecialization: number of constants exceed "
+                    << "the maximum number of constants threshold.\n"
+                    << "Truncating worklist to " << MaxConstantsThreshold
+                    << " candidates.\n");
+        Worklist.erase(Worklist.begin() + MaxConstantsThreshold,
+                       Worklist.end());
       }
 
       if (IsPartial || Worklist.size() < ActualConstArg.size())
Index: llvm/test/Transforms/FunctionSpecialization/function-specialization4.ll
===================================================================
--- llvm/test/Transforms/FunctionSpecialization/function-specialization4.ll
+++ llvm/test/Transforms/FunctionSpecialization/function-specialization4.ll
@@ -38,7 +38,7 @@
   ret i32 %add1
 }
 
-; CONST1-NOT: define internal i32 @foo.1(i32 %x, i32* %b, i32* %c)
+; CONST1:     define internal i32 @foo.1(i32 %x, i32* %b, i32* %c)
 ; CONST1-NOT: define internal i32 @foo.2(i32 %x, i32* %b, i32* %c)
 
 ; CHECK:        define internal i32 @foo.1(i32 %x, i32* %b, i32* %c) {