diff --git a/clang-tools-extra/clangd/unittests/CodeCompleteTests.cpp b/clang-tools-extra/clangd/unittests/CodeCompleteTests.cpp
--- a/clang-tools-extra/clangd/unittests/CodeCompleteTests.cpp
+++ b/clang-tools-extra/clangd/unittests/CodeCompleteTests.cpp
@@ -2297,6 +2297,16 @@
                            AllOf(Named("TestClangc"), Deprecated())));
 }
 
+TEST(SignatureHelpTest, PartialSpec) {
+  const auto Results = signatures(R"cpp(
+      template <typename T> struct Foo {};
+      template <typename T> struct Foo<T*> { Foo(T); };
+      Foo<int*> F(^);
+    )cpp");
+  EXPECT_THAT(Results.signatures, Contains(Sig("Foo([[T]])")));
+  EXPECT_EQ(0, Results.activeParameter);
+}
+
 TEST(SignatureHelpTest, InsideArgument) {
   {
     const auto Results = signatures(R"cpp(
diff --git a/clang/test/CodeCompletion/ctor-signature.cpp b/clang/test/CodeCompletion/ctor-signature.cpp
new file mode 100644
--- /dev/null
+++ b/clang/test/CodeCompletion/ctor-signature.cpp
@@ -0,0 +1,17 @@
+template <typename T>
+struct Foo {};
+template <typename T>
+struct Foo<T *> { Foo(T); };
+
+void foo() {
+  Foo<int>();
+  // RUN: %clang_cc1 -fsyntax-only -code-completion-at=%s:7:12 %s -o - | FileCheck -check-prefix=CHECK-CC1 %s
+  // CHECK-CC1: OVERLOAD: Foo()
+  // CHECK-CC1: OVERLOAD: Foo(<#const Foo<int> &#>)
+  // CHECK-CC1: OVERLOAD: Foo(<#Foo<int> &&#>
+  Foo<int *>(3);
+  // RUN: %clang_cc1 -fsyntax-only -code-completion-at=%s:12:14 %s -o - | FileCheck -check-prefix=CHECK-CC2 %s
+  // CHECK-CC2: OVERLOAD: Foo(<#int#>)
+  // CHECK-CC2: OVERLOAD: Foo(<#const Foo<int *> &#>)
+  // CHECK-CC2: OVERLOAD: Foo(<#Foo<int *> &&#>
+}