diff --git a/llvm/lib/Transforms/IPO/FunctionSpecialization.cpp b/llvm/lib/Transforms/IPO/FunctionSpecialization.cpp
--- a/llvm/lib/Transforms/IPO/FunctionSpecialization.cpp
+++ b/llvm/lib/Transforms/IPO/FunctionSpecialization.cpp
@@ -12,7 +12,7 @@
 //
 // Current limitations:
 // - It does not handle specialization of recursive functions,
-// - It does not yet handle integer constants, and integer ranges,
+// - It does not yet handle integer ranges.
 // - Only 1 argument per function is specialised,
 // - The cost-model could be further looked into,
 // - We are not yet caching analysis results.
@@ -64,6 +64,10 @@
                           cl::desc("Average loop iteration count cost"),
                           cl::init(10));
 
+static cl::opt<bool> EnableSpecializationForLiteralConstant(
+    "function-specialization-for-literal-constant", cl::init(false), cl::Hidden,
+    cl::desc("Make function specialization available for literal constant."));
+
 // Helper to check if \p LV is either overdefined or a constant int.
 static bool isOverdefined(const ValueLatticeElement &LV) {
   return !LV.isUnknownOrUndef() && !LV.isConstant();
@@ -485,17 +489,11 @@
         }
       }
 
-      // Get the lattice value for the value the call site passes to the
-      // argument. If this value is not constant, move on to the next call
-      // site. Additionally, set the AllConstant flag to false.
-      if (V != A && !Solver.getLatticeValueFor(V).isConstant()) {
+      if (isa<Constant>(V) && (Solver.getLatticeValueFor(V).isConstant() ||
+                               EnableSpecializationForLiteralConstant))
+        Constants.push_back(cast<Constant>(V));
+      else
         AllConstant = false;
-        continue;
-      }
-
-      // Add the constant to the set.
-      if (auto *C = dyn_cast<Constant>(CS.getArgOperand(A->getArgNo())))
-        Constants.push_back(C);
     }
 
     // If the argument can only take on constant values, AllConstant will be
diff --git a/llvm/test/Transforms/FunctionSpecialization/function-specialization-constant-integers.ll b/llvm/test/Transforms/FunctionSpecialization/function-specialization-constant-integers.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/FunctionSpecialization/function-specialization-constant-integers.ll
@@ -0,0 +1,44 @@
+; RUN: opt -function-specialization -function-specialization-for-literal-constant=true -S < %s | FileCheck %s
+
+; Check that the literal constant parameter could be specialized.
+; CHECK: @foo.1(
+; CHECK: @foo.2(
+
+target datalayout = "e-m:e-i8:8:32-i16:16:32-i64:64-i128:128-n32:64-S128"
+
+declare i32 @getValue()
+declare i1 @getCond()
+
+define internal i32 @foo(i1 %break_cond) {
+entry:
+  br label %loop.entry
+
+loop.entry:
+  br label %loop2.entry
+
+loop2.entry:
+  br label %loop2.body
+
+loop2.body:
+  %value = call i32 @getValue()
+  br i1 %break_cond, label %loop2.end, label %return
+
+loop2.end:
+  %cond.end = call i1 @getCond()
+  br i1 %cond.end, label %loop2.entry, label %loop.end
+
+loop.end:
+  %cond2.end = call i1 @getCond()
+  br i1 %cond2.end, label %loop.entry, label %return
+
+return:
+  ret i32 %value
+}
+
+define dso_local i32 @bar(i32 %x, i32 %y) {
+entry:
+  %retval.1 = call i32 @foo(i1 1)
+  %retval.2 = call i32 @foo(i1 0)
+  %retval = add nsw i32 %retval.1, %retval.2
+  ret i32 %retval
+}
\ No newline at end of file