diff --git a/clang/lib/Sema/SemaCodeComplete.cpp b/clang/lib/Sema/SemaCodeComplete.cpp
index 4575d4fe4675..d2e7766f8f15 100644
--- a/clang/lib/Sema/SemaCodeComplete.cpp
+++ b/clang/lib/Sema/SemaCodeComplete.cpp
@@ -16,7 +16,9 @@
 #include "clang/AST/ExprCXX.h"
 #include "clang/AST/ExprObjC.h"
 #include "clang/AST/QualTypeNames.h"
+#include "clang/AST/Type.h"
 #include "clang/Basic/CharInfo.h"
+#include "clang/Basic/Specifiers.h"
 #include "clang/Lex/HeaderSearch.h"
 #include "clang/Lex/MacroInfo.h"
 #include "clang/Lex/Preprocessor.h"
@@ -82,6 +84,15 @@ private:
 
   public:
     ShadowMapEntry() : DeclOrVector(), SingleDeclIndex(0) {}
+    ShadowMapEntry(const ShadowMapEntry &) = delete;
+    ShadowMapEntry(ShadowMapEntry &&Move) { *this = std::move(Move); }
+    ShadowMapEntry &operator=(const ShadowMapEntry &) = delete;
+    ShadowMapEntry &operator=(ShadowMapEntry &&Move) {
+      SingleDeclIndex = Move.SingleDeclIndex;
+      DeclOrVector = Move.DeclOrVector;
+      Move.DeclOrVector = nullptr;
+      return *this;
+    }
 
     void Add(const NamedDecl *ND, unsigned Index) {
       if (DeclOrVector.isNull()) {
@@ -105,7 +116,7 @@ private:
           DeclIndexPair(ND, Index));
     }
 
-    void Destroy() {
+    ~ShadowMapEntry() {
       if (DeclIndexPairVector *Vec =
               DeclOrVector.dyn_cast<DeclIndexPairVector *>()) {
         delete Vec;
@@ -152,9 +163,16 @@ private:
   /// different levels of, e.g., the inheritance hierarchy.
   std::list<ShadowMap> ShadowMaps;
 
+  /// Overloaded C++ member functions found by SemaLookup.
+  /// Used to determine when one overload is dominated by another.
+  llvm::DenseMap<std::pair<DeclContext *, /*Name*/uintptr_t>, ShadowMapEntry>
+      OverloadMap;
+
   /// If we're potentially referring to a C++ member function, the set
   /// of qualifiers applied to the object type.
   Qualifiers ObjectTypeQualifiers;
+  /// The kind of the object expression, for rvalue/lvalue overloads.
+  ExprValueKind ObjectKind;
 
   /// Whether the \p ObjectTypeQualifiers field is active.
   bool HasObjectTypeQualifiers;
@@ -230,8 +248,9 @@ public:
   /// out member functions that aren't available (because there will be a
   /// cv-qualifier mismatch) or prefer functions with an exact qualifier
   /// match.
-  void setObjectTypeQualifiers(Qualifiers Quals) {
+  void setObjectTypeQualifiers(Qualifiers Quals, ExprValueKind Kind) {
     ObjectTypeQualifiers = Quals;
+    ObjectKind = Kind;
     HasObjectTypeQualifiers = true;
   }
 
@@ -1157,6 +1176,53 @@ static void setInBaseClass(ResultBuilder::Result &R) {
   R.InBaseClass = true;
 }
 
+enum class OverloadCompare { BothViable, Dominates, Dominated };
+// Will Candidate ever be called on the object, when overloaded with Incumbent?
+// Returns Dominates if Candidate is always called, Dominated if Incumbent is
+// always called, BothViable if either may be called dependending on arguments.
+// Precondition: must actually be overloads!
+static OverloadCompare compareOverloads(const CXXMethodDecl &Candidate,
+                                        const CXXMethodDecl &Incumbent,
+                                        const Qualifiers &ObjectQuals,
+                                        ExprValueKind ObjectKind) {
+  if (Candidate.isVariadic() != Incumbent.isVariadic() ||
+      Candidate.getNumParams() != Incumbent.getNumParams() ||
+      Candidate.getMinRequiredArguments() !=
+          Incumbent.getMinRequiredArguments())
+    return OverloadCompare::BothViable;
+  for (unsigned I = 0, E = Candidate.getNumParams(); I != E; ++I)
+    if (Candidate.parameters()[I]->getType().getCanonicalType() !=
+        Incumbent.parameters()[I]->getType().getCanonicalType())
+      return OverloadCompare::BothViable;
+  if (!llvm::empty(Candidate.specific_attrs<EnableIfAttr>()) ||
+      !llvm::empty(Incumbent.specific_attrs<EnableIfAttr>()))
+    return OverloadCompare::BothViable;
+  // At this point, we know calls can't pick one or the other based on
+  // arguments, so one of the two must win. (Or both fail, handled elsewhere).
+  RefQualifierKind CandidateRef = Candidate.getRefQualifier();
+  RefQualifierKind IncumbentRef = Incumbent.getRefQualifier();
+  if (CandidateRef != IncumbentRef) {
+    // If the object kind is LValue/RValue, there's one acceptable ref-qualifier
+    // and it can't be mixed with ref-unqualified overloads (in valid code).
+
+    // For xvalue objects, we prefer the rvalue overload even if we have to
+    // add qualifiers (which is rare, because const&& is rare).
+    if (ObjectKind == clang::VK_XValue)
+      return CandidateRef == RQ_RValue ? OverloadCompare::Dominates
+                                       : OverloadCompare::Dominated;
+  }
+  // Now the ref qualifiers are the same (or we're in some invalid state).
+  // So make some decision based on the qualifiers.
+  Qualifiers CandidateQual = Candidate.getMethodQualifiers();
+  Qualifiers IncumbentQual = Incumbent.getMethodQualifiers();
+  bool CandidateSuperset = CandidateQual.compatiblyIncludes(IncumbentQual);
+  bool IncumbentSuperset = IncumbentQual.compatiblyIncludes(CandidateQual);
+  if (CandidateSuperset == IncumbentSuperset)
+    return OverloadCompare::BothViable;
+  return IncumbentSuperset ? OverloadCompare::Dominates
+                           : OverloadCompare::Dominated;
+}
+
 void ResultBuilder::AddResult(Result R, DeclContext *CurContext,
                               NamedDecl *Hiding, bool InBaseClass = false) {
   if (R.Kind != Result::RK_Declaration) {
@@ -1233,6 +1299,44 @@ void ResultBuilder::AddResult(Result R, DeclContext *CurContext,
           // qualifiers.
           return;
         }
+        // Detect cases where a ref-qualified method cannot be invoked.
+        switch (Method->getRefQualifier()) {
+          case RQ_LValue:
+            if (ObjectKind != VK_LValue && !MethodQuals.hasConst())
+              return;
+            break;
+          case RQ_RValue:
+            if (ObjectKind == VK_LValue)
+              return;
+            break;
+          case RQ_None:
+            break;
+        }
+
+        /// Check whether this dominates another overloaded method, which should
+        /// be suppressed (or vice versa).
+        /// Motivating case is const_iterator begin() const vs iterator begin().
+        auto &OverloadSet = OverloadMap[std::make_pair(
+            CurContext, Method->getDeclName().getAsOpaqueInteger())];
+        for (const DeclIndexPair& Entry : OverloadSet) {
+          Result &Incumbent = Results[Entry.second];
+          switch (compareOverloads(*Method,
+                                   *cast<CXXMethodDecl>(Incumbent.Declaration),
+                                   ObjectTypeQualifiers, ObjectKind)) {
+          case OverloadCompare::Dominates:
+            // Replace the dominated overload with this one.
+            // FIXME: if the overload dominates multiple incumbents then we
+            // should remove all. But two overloads is by far the common case.
+            Incumbent = std::move(R);
+            return;
+          case OverloadCompare::Dominated:
+            // This overload can't be called, drop it.
+            return;
+          case OverloadCompare::BothViable:
+            break;
+          }
+        }
+        OverloadSet.Add(Method, Results.size());
       }
 
   // Insert this result into the set of results.
@@ -1253,11 +1357,6 @@ void ResultBuilder::EnterNewScope() { ShadowMaps.emplace_back(); }
 
 /// Exit from the current scope.
 void ResultBuilder::ExitScope() {
-  for (ShadowMap::iterator E = ShadowMaps.back().begin(),
-                           EEnd = ShadowMaps.back().end();
-       E != EEnd; ++E)
-    E->second.Destroy();
-
   ShadowMaps.pop_back();
 }
 
@@ -3997,7 +4096,8 @@ void Sema::CodeCompleteOrdinaryName(Scope *S,
   // the member function to filter/prioritize the results list.
   auto ThisType = getCurrentThisType();
   if (!ThisType.isNull())
-    Results.setObjectTypeQualifiers(ThisType->getPointeeType().getQualifiers());
+    Results.setObjectTypeQualifiers(ThisType->getPointeeType().getQualifiers(),
+                                    VK_LValue);
 
   CodeCompletionDeclConsumer Consumer(Results, CurContext);
   LookupVisibleDecls(S, LookupOrdinaryName, Consumer,
@@ -4551,13 +4651,12 @@ AddObjCProperties(const CodeCompletionContext &CCContext,
   }
 }
 
-static void
-AddRecordMembersCompletionResults(Sema &SemaRef, ResultBuilder &Results,
-                                  Scope *S, QualType BaseType, RecordDecl *RD,
-                                  Optional<FixItHint> AccessOpFixIt) {
+static void AddRecordMembersCompletionResults(
+    Sema &SemaRef, ResultBuilder &Results, Scope *S, QualType BaseType,
+    ExprValueKind BaseKind, RecordDecl *RD, Optional<FixItHint> AccessOpFixIt) {
   // Indicate that we are performing a member access, and the cv-qualifiers
   // for the base object type.
-  Results.setObjectTypeQualifiers(BaseType.getQualifiers());
+  Results.setObjectTypeQualifiers(BaseType.getQualifiers(), BaseKind);
 
   // Access to a C/C++ class, struct, or union.
   Results.allowNestedNameSpecifiers();
@@ -4638,18 +4737,20 @@ void Sema::CodeCompleteMemberReferenceExpr(Scope *S, Expr *Base,
     Base = ConvertedBase.get();
 
     QualType BaseType = Base->getType();
+    ExprValueKind BaseKind = Base->getValueKind();
 
     if (IsArrow) {
-      if (const PointerType *Ptr = BaseType->getAs<PointerType>())
+      if (const PointerType *Ptr = BaseType->getAs<PointerType>()) {
         BaseType = Ptr->getPointeeType();
-      else if (BaseType->isObjCObjectPointerType())
+        BaseKind = VK_LValue;
+      } else if (BaseType->isObjCObjectPointerType())
         /*Do nothing*/;
       else
         return false;
     }
 
     if (const RecordType *Record = BaseType->getAs<RecordType>()) {
-      AddRecordMembersCompletionResults(*this, Results, S, BaseType,
+      AddRecordMembersCompletionResults(*this, Results, S, BaseType, BaseKind,
                                         Record->getDecl(),
                                         std::move(AccessOpFixIt));
     } else if (const auto *TST =
@@ -4658,13 +4759,13 @@ void Sema::CodeCompleteMemberReferenceExpr(Scope *S, Expr *Base,
       if (const auto *TD =
               dyn_cast_or_null<ClassTemplateDecl>(TN.getAsTemplateDecl())) {
         CXXRecordDecl *RD = TD->getTemplatedDecl();
-        AddRecordMembersCompletionResults(*this, Results, S, BaseType, RD,
-                                          std::move(AccessOpFixIt));
+        AddRecordMembersCompletionResults(*this, Results, S, BaseType, BaseKind,
+                                          RD, std::move(AccessOpFixIt));
       }
     } else if (const auto *ICNT = BaseType->getAs<InjectedClassNameType>()) {
       if (auto *RD = ICNT->getDecl())
-        AddRecordMembersCompletionResults(*this, Results, S, BaseType, RD,
-                                          std::move(AccessOpFixIt));
+        AddRecordMembersCompletionResults(*this, Results, S, BaseType, BaseKind,
+                                          RD, std::move(AccessOpFixIt));
     } else if (!IsArrow && BaseType->isObjCObjectPointerType()) {
       // Objective-C property reference.
       AddedPropertiesSet AddedProperties;
diff --git a/clang/test/CodeCompletion/member-access.cpp b/clang/test/CodeCompletion/member-access.cpp
index 003d224fbe24..6d7cf6ac7cd7 100644
--- a/clang/test/CodeCompletion/member-access.cpp
+++ b/clang/test/CodeCompletion/member-access.cpp
@@ -210,3 +210,66 @@ void test3(const Proxy2 &p) {
 // CHECK-CC9: memfun2 (InBase) : [#void#][#Base3::#]memfun2(<#int#>) (requires fix-it: {181:4-181:5} to "->")
 // CHECK-CC9: memfun3 : [#int#]memfun3(<#int#>) (requires fix-it: {181:4-181:5} to "->")
 // CHECK-CC9: operator-> : [#Derived *#]operator->()[# const#]
+
+// These overload sets differ only by return type and this-qualifiers.
+// So for any given callsite, only one is available.
+struct Overloads {
+  double ConstOverload(char);
+  int ConstOverload(char) const;
+
+  int RefOverload(char) &;
+  double RefOverload(char) const&;
+  char RefOverload(char) &&;
+};
+void testLValue(Overloads& Ref) {
+  Ref.
+}
+void testConstLValue(const Overloads& ConstRef) {
+  ConstRef.
+}
+void testRValue() {
+  Overloads().
+}
+void testXValue(Overloads& X) {
+  static_cast<Overloads&&>(X).
+}
+
+// RUN: %clang_cc1 -fsyntax-only -code-completion-at=%s:225:7 %s -o - | FileCheck -check-prefix=CHECK-LVALUE %s \
+// RUN: --implicit-check-not="[#int#]ConstOverload(" \
+// RUN: --implicit-check-not="[#double#]RefOverload(" \
+// RUN: --implicit-check-not="[#char#]RefOverload("
+// CHECK-LVALUE-DAG: [#double#]ConstOverload(
+// CHECK-LVALUE-DAG: [#int#]RefOverload(
+
+// RUN: %clang_cc1 -fsyntax-only -code-completion-at=%s:228:12 %s -o - | FileCheck -check-prefix=CHECK-CONSTLVALUE %s \
+// RUN: --implicit-check-not="[#double#]ConstOverload(" \
+// RUN: --implicit-check-not="[#int#]RefOverload(" \
+// RUN: --implicit-check-not="[#char#]RefOverload("
+// CHECK-CONSTLVALUE: [#int#]ConstOverload(
+// CHECK-CONSTLVALUE: [#double#]RefOverload(
+
+// RUN: %clang_cc1 -fsyntax-only -code-completion-at=%s:231:15 %s -o - | FileCheck -check-prefix=CHECK-PRVALUE %s \
+// RUN: --implicit-check-not="[#int#]ConstOverload(" \
+// RUN: --implicit-check-not="[#int#]RefOverload(" \
+// RUN: --implicit-check-not="[#double#]RefOverload("
+// CHECK-PRVALUE: [#double#]ConstOverload(
+// CHECK-PRVALUE: [#char#]RefOverload(
+
+// RUN: %clang_cc1 -fsyntax-only -code-completion-at=%s:234:31 %s -o - | FileCheck -check-prefix=CHECK-XVALUE %s \
+// RUN: --implicit-check-not="[#int#]ConstOverload(" \
+// RUN: --implicit-check-not="[#int#]RefOverload(" \
+// RUN: --implicit-check-not="[#double#]RefOverload("
+// CHECK-XVALUE: [#double#]ConstOverload(
+// CHECK-XVALUE: [#char#]RefOverload(
+
+void testOverloadOperator() {
+  struct S {
+    char operator=(int) const;
+    int operator=(int);
+  } s;
+  return s.
+}
+// RUN: %clang_cc1 -fsyntax-only -code-completion-at=%s:270:12 %s -o - | FileCheck -check-prefix=CHECK-OPER %s \
+// RUN: --implicit-check-not="[#char#]operator=("
+// CHECK-OPER: [#int#]operator=(
+