diff --git a/clang-tools-extra/clangd/AST.cpp b/clang-tools-extra/clangd/AST.cpp
--- a/clang-tools-extra/clangd/AST.cpp
+++ b/clang-tools-extra/clangd/AST.cpp
@@ -127,6 +127,8 @@
   std::string Name;
   llvm::raw_string_ostream Out(Name);
   PrintingPolicy PP(Ctx.getLangOpts());
+  // We don't consider a class template's args part of the constructor name.
+  PP.SuppressTemplateArgsInCXXConstructors = true;
 
   // Handle 'using namespace'. They all have the same name - <using-directive>.
   if (auto *UD = llvm::dyn_cast<UsingDirectiveDecl>(&ND)) {
diff --git a/clang-tools-extra/clangd/XRefs.cpp b/clang-tools-extra/clangd/XRefs.cpp
--- a/clang-tools-extra/clangd/XRefs.cpp
+++ b/clang-tools-extra/clangd/XRefs.cpp
@@ -417,6 +417,7 @@
   auto GetName = [](const Decl *D) {
     const NamedDecl *ND = dyn_cast<NamedDecl>(D);
     std::string Name = ND->getNameAsString();
+    // FIXME(sammccall): include template params/specialization args?.
     if (!Name.empty())
       return Name;
     if (auto RD = dyn_cast<RecordDecl>(D))
diff --git a/clang-tools-extra/clangd/unittests/XRefsTests.cpp b/clang-tools-extra/clangd/unittests/XRefsTests.cpp
--- a/clang-tools-extra/clangd/unittests/XRefsTests.cpp
+++ b/clang-tools-extra/clangd/unittests/XRefsTests.cpp
@@ -897,7 +897,7 @@
          HI.Definition = "int test";
          HI.Type = "int";
        }},
-      // Partially-specialized class decl. (formerly type-parameter-0-0)
+      // Partially-specialized class template. (formerly type-parameter-0-0)
       {R"cpp(
         template <typename T> class X;
         template <typename T> class [[^X]]<T*> {};
@@ -908,6 +908,21 @@
          HI.Kind = SymbolKind::Class;
          HI.Definition = "template <typename T> class X<T *> {}";
        }},
+      // Constructor of partially-specialized class template
+      {R"cpp(
+          template<typename> struct X;
+          template<typename T> struct X<T*>{ [[^X]](); };
+          )cpp",
+       [](HoverInfo &HI) {
+         HI.NamespaceScope = "";
+         HI.Name = "X";
+         HI.LocalScope = "X::";        // FIXME: Should be X<T *>::
+         HI.Kind = SymbolKind::Method; // FIXME: Should be Constructor
+         HI.Type = "void ()";          // FIXME: Should be None
+         HI.ReturnType = "void";       // FIXME: Should be None or X<T*>
+         HI.Definition = "X<type - parameter - 0 - 0 *>()"; // FIXME: --> X()
+         HI.Parameters.emplace();
+       }},
 
       // auto on lambda
       {R"cpp(