diff --git a/llvm/test/Transforms/FunctionSpecialization/no-spec-unused-arg.ll b/llvm/test/Transforms/FunctionSpecialization/no-spec-unused-arg.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/FunctionSpecialization/no-spec-unused-arg.ll
@@ -0,0 +1,20 @@
+; RUN: opt -S --passes=function-specialization -force-function-specialization -function-specialization-for-literal-constant < %s | FileCheck %s
+define internal i32 @f(i32 %x, i32 %y) noinline {
+    ret i32 %x
+}
+
+define i32 @g0() {
+    %r = call i32 @f(i32 1, i32 1)
+    ret i32 %r
+}
+
+define i32 @g1() {
+    %r = call i32 @f(i32 1, i32 2)
+    ret i32 %r
+}
+
+; Check that there are no specialisation of `f`: first parameter is deduced
+; to be a constant without the need for function specialisation and
+; the second parameter is unused.
+
+;  CHECK-NOT: @f.
\ No newline at end of file