diff --git a/clang/include/clang/AST/Type.h b/clang/include/clang/AST/Type.h
index ce1ce54d1560..9eb6d81296d8 100644
--- a/clang/include/clang/AST/Type.h
+++ b/clang/include/clang/AST/Type.h
@@ -2011,10 +2011,11 @@ public:
   Optional<NullabilityKind> getNullability(const ASTContext &context) const;
 
   /// Determine whether the given type can have a nullability
-  /// specifier applied to it, i.e., if it is any kind of pointer type
-  /// or a dependent type that could instantiate to any kind of
-  /// pointer type.
-  bool canHaveNullability() const;
+  /// specifier applied to it, i.e., if it is any kind of pointer type.
+  ///
+  /// \param ResultIfUnknown The value to return if we don't yet know whether
+  ///        this type can have nullability because it is dependent.
+  bool canHaveNullability(bool ResultIfUnknown = true) const;
 
   /// Retrieve the set of substitutions required when accessing a member
   /// of the Objective-C receiver type that is declared in the given context.
diff --git a/clang/lib/AST/Type.cpp b/clang/lib/AST/Type.cpp
index 22d52bcd3f31..1e10094aeeea 100644
--- a/clang/lib/AST/Type.cpp
+++ b/clang/lib/AST/Type.cpp
@@ -3531,7 +3531,7 @@ Optional<NullabilityKind> Type::getNullability(const ASTContext &context) const
   } while (true);
 }
 
-bool Type::canHaveNullability() const {
+bool Type::canHaveNullability(bool ResultIfUnknown) const {
   QualType type = getCanonicalTypeInternal();
   
   switch (type->getTypeClass()) {
@@ -3559,7 +3559,8 @@ bool Type::canHaveNullability() const {
   case Type::SubstTemplateTypeParmPack:
   case Type::DependentName:
   case Type::DependentTemplateSpecialization:
-    return true;
+  case Type::Auto:
+    return ResultIfUnknown;
 
   // Dependent template specializations can instantiate to pointer
   // types unless they're known to be specializations of a class
@@ -3571,12 +3572,7 @@ bool Type::canHaveNullability() const {
       if (isa<ClassTemplateDecl>(templateDecl))
         return false;
     }
-    return true;
-
-  // auto is considered dependent when it isn't deduced.
-  case Type::Auto:
-  case Type::DeducedTemplateSpecialization:
-    return !cast<DeducedType>(type.getTypePtr())->isDeduced();
+    return ResultIfUnknown;
 
   case Type::Builtin:
     switch (cast<BuiltinType>(type.getTypePtr())->getKind()) {
@@ -3595,7 +3591,7 @@ bool Type::canHaveNullability() const {
     case BuiltinType::PseudoObject:
     case BuiltinType::UnknownAny:
     case BuiltinType::ARCUnbridgedCast:
-      return true;
+      return ResultIfUnknown;
 
     case BuiltinType::Void:
     case BuiltinType::ObjCId:
@@ -3614,6 +3610,7 @@ bool Type::canHaveNullability() const {
     case BuiltinType::OMPArraySection:
       return false;
     }
+    llvm_unreachable("unknown builtin type");
 
   // Non-pointer types.
   case Type::Complex:
@@ -3629,6 +3626,7 @@ bool Type::canHaveNullability() const {
   case Type::FunctionProto:
   case Type::FunctionNoProto:
   case Type::Record:
+  case Type::DeducedTemplateSpecialization:
   case Type::Enum:
   case Type::InjectedClassName:
   case Type::PackExpansion:
diff --git a/clang/lib/Sema/SemaType.cpp b/clang/lib/Sema/SemaType.cpp
index 1433607e9c71..f8970744389b 100644
--- a/clang/lib/Sema/SemaType.cpp
+++ b/clang/lib/Sema/SemaType.cpp
@@ -3735,16 +3735,8 @@ static TypeSourceInfo *GetFullTypeForDeclarator(TypeProcessingState &state,
     // inner pointers.
     complainAboutMissingNullability = CAMN_InnerPointers;
 
-    auto isDependentNonPointerType = [](QualType T) -> bool {
-      // Note: This is intended to be the same check as Type::canHaveNullability
-      // except with all of the ambiguous cases being treated as 'false' rather
-      // than 'true'.
-      return T->isDependentType() && !T->isAnyPointerType() &&
-        !T->isBlockPointerType() && !T->isMemberPointerType();
-    };
-
-    if (T->canHaveNullability() && !T->getNullability(S.Context) &&
-        !isDependentNonPointerType(T)) {
+    if (T->canHaveNullability(/*ResultIfUnknown*/false) &&
+        !T->getNullability(S.Context)) {
       // Note that we allow but don't require nullability on dependent types.
       ++NumPointersRemaining;
     }
@@ -3962,7 +3954,8 @@ static TypeSourceInfo *GetFullTypeForDeclarator(TypeProcessingState &state,
   // If the type itself could have nullability but does not, infer pointer
   // nullability and perform consistency checking.
   if (S.CodeSynthesisContexts.empty()) {
-    if (T->canHaveNullability() && !T->getNullability(S.Context)) {
+    if (T->canHaveNullability(/*ResultIfUnknown*/false) &&
+        !T->getNullability(S.Context)) {
       if (isVaList(T)) {
         // Record that we've seen a pointer, but do nothing else.
         if (NumPointersRemaining > 0)
diff --git a/clang/test/SemaCXX/Inputs/nullability-completeness.h b/clang/test/SemaCXX/Inputs/nullability-completeness.h
new file mode 100644
index 000000000000..1b30e1b4d906
--- /dev/null
+++ b/clang/test/SemaCXX/Inputs/nullability-completeness.h
@@ -0,0 +1,4 @@
+template<typename T> struct Template final {
+  int *_Nonnull x;
+  T y;
+};
diff --git a/clang/test/SemaCXX/nullability.cpp b/clang/test/SemaCXX/nullability.cpp
index 160741b1409c..99375a9fdde3 100644
--- a/clang/test/SemaCXX/nullability.cpp
+++ b/clang/test/SemaCXX/nullability.cpp
@@ -1,10 +1,12 @@
-// RUN: %clang_cc1 -std=c++11 -fsyntax-only -Wno-nullability-declspec %s -verify -Wnullable-to-nonnull-conversion
+// RUN: %clang_cc1 -std=c++11 -fsyntax-only -Wno-nullability-declspec %s -verify -Wnullable-to-nonnull-conversion -I%S/Inputs
 
 #if __has_feature(nullability)
 #else
 #  error nullability feature should be defined
 #endif
 
+#include "nullability-completeness.h"
+
 typedef decltype(nullptr) nullptr_t;
 
 class X {
@@ -130,3 +132,7 @@ void arraysInLambdas() {
   withTypedef(nullptr); // expected-warning {{null passed to a callee that requires a non-null argument}}
   auto withTypedefBad = [](INTS _Nonnull[2]) {}; // expected-error {{nullability specifier '_Nonnull' cannot be applied to non-pointer type 'INTS' (aka 'int [4]')}}
 }
+
+void testNullabilityCompletenessWithTemplate() {
+  Template<int*> tip;
+}