diff --git a/lib/ClangImporter/ClangImporter.cpp b/lib/ClangImporter/ClangImporter.cpp
index 3f422f48d5b87..cf05fcd56ccf4 100644
--- a/lib/ClangImporter/ClangImporter.cpp
+++ b/lib/ClangImporter/ClangImporter.cpp
@@ -7368,12 +7368,6 @@ static bool hasDestroyTypeOperations(const clang::CXXRecordDecl *decl) {
 }
 
 static bool hasCustomCopyOrMoveConstructor(const clang::CXXRecordDecl *decl) {
-  // std::pair and std::tuple might have copy and move constructors, but that
-  // doesn't mean they are safe to use from Swift, e.g. std::pair<UnsafeType, T>
-  if (decl->isInStdNamespace() &&
-      (decl->getName() == "pair" || decl->getName() == "tuple")) {
-    return false;
-  }
   return decl->hasUserDeclaredCopyConstructor() ||
          decl->hasUserDeclaredMoveConstructor();
 }
@@ -7489,6 +7483,13 @@ CxxRecordAsSwiftType::evaluate(Evaluator &evaluator,
 }
 
 bool anySubobjectsSelfContained(const clang::CXXRecordDecl *decl) {
+  // std::pair and std::tuple might have copy and move constructors, or base
+  // classes with copy and move constructors, but they are not self-contained
+  // types, e.g. `std::pair<UnsafeType, T>`.
+  if (decl->isInStdNamespace() &&
+      (decl->getName() == "pair" || decl->getName() == "tuple"))
+    return false;
+
   if (!decl->getDefinition())
     return false;
 
diff --git a/lib/ClangImporter/ImportDecl.cpp b/lib/ClangImporter/ImportDecl.cpp
index 8b782a8750e79..cc33d2a20703d 100644
--- a/lib/ClangImporter/ImportDecl.cpp
+++ b/lib/ClangImporter/ImportDecl.cpp
@@ -2959,9 +2959,7 @@ namespace {
         if (notInstantiated)
           return nullptr;
       }
-      if (!clangSema.isCompleteType(
-              decl->getLocation(),
-              Impl.getClangASTContext().getRecordType(decl))) {
+      if (!decl->getDefinition()) {
         // If we got nullptr definition now it means the type is not complete.
         // We don't import incomplete types.
         return nullptr;
diff --git a/test/Interop/Cxx/stdlib/Inputs/module.modulemap b/test/Interop/Cxx/stdlib/Inputs/module.modulemap
index 3092b15d76a42..187111acca6a2 100644
--- a/test/Interop/Cxx/stdlib/Inputs/module.modulemap
+++ b/test/Interop/Cxx/stdlib/Inputs/module.modulemap
@@ -1,26 +1,31 @@
 module StdVector {
   header "std-vector.h"
   requires cplusplus
+  export *
 }
 
 module StdMap {
   header "std-map.h"
   requires cplusplus
+  export *
 }
 
 module StdOptional {
   header "std-optional.h"
   requires cplusplus
+  export *
 }
 
 module StdSet {
   header "std-set.h"
   requires cplusplus
+  export *
 }
 
 module StdPair {
   header "std-pair.h"
   requires cplusplus
+  export *
 }
 
 module MsvcUseVecIt {
@@ -32,4 +37,11 @@ module MsvcUseVecIt {
 module StdUniquePtr {
   header "std-unique-ptr.h"
   requires cplusplus
+  export *
+}
+
+module StdFunction {
+  header "std-function.h"
+  requires cplusplus
+  export *
 }
diff --git a/test/Interop/Cxx/stdlib/Inputs/std-function.h b/test/Interop/Cxx/stdlib/Inputs/std-function.h
new file mode 100644
index 0000000000000..1486f3a3e20de
--- /dev/null
+++ b/test/Interop/Cxx/stdlib/Inputs/std-function.h
@@ -0,0 +1,16 @@
+#ifndef TEST_INTEROP_CXX_STDLIB_INPUTS_STD_FUNCTION_H
+#define TEST_INTEROP_CXX_STDLIB_INPUTS_STD_FUNCTION_H
+
+#include <functional>
+
+using FunctionIntToInt = std::function<int(int)>;
+
+FunctionIntToInt getIdentityFunction() {
+  return [](int x) { return x; };
+}
+
+bool isEmptyFunction(FunctionIntToInt f) { return !(bool)f; }
+
+int invokeFunction(FunctionIntToInt f, int x) { return f(x); }
+
+#endif // TEST_INTEROP_CXX_STDLIB_INPUTS_STD_FUNCTION_H
diff --git a/test/Interop/Cxx/stdlib/Inputs/std-pair.h b/test/Interop/Cxx/stdlib/Inputs/std-pair.h
index 8fc2604600e32..ff0c213b8a778 100644
--- a/test/Interop/Cxx/stdlib/Inputs/std-pair.h
+++ b/test/Interop/Cxx/stdlib/Inputs/std-pair.h
@@ -35,7 +35,7 @@ struct __attribute__((swift_attr("import_iterator"))) Iterator {};
 using PairUnsafeStructInt = std::pair<UnsafeStruct, int>;
 using PairIteratorInt = std::pair<Iterator, int>;
 
-struct HasMethodThatReturnsUnsafePair {
+struct __attribute__((swift_attr("import_owned"))) HasMethodThatReturnsUnsafePair {
     PairUnsafeStructInt getUnsafePair() const { return {}; }
     PairIteratorInt getIteratorPair() const { return {}; }
 };
diff --git a/test/Interop/Cxx/stdlib/use-std-function.swift b/test/Interop/Cxx/stdlib/use-std-function.swift
new file mode 100644
index 0000000000000..271a89b8f8982
--- /dev/null
+++ b/test/Interop/Cxx/stdlib/use-std-function.swift
@@ -0,0 +1,29 @@
+// RUN: %target-run-simple-swift(-I %S/Inputs -Xfrontend -enable-experimental-cxx-interop)
+// RUN: %target-run-simple-swift(-I %S/Inputs -cxx-interoperability-mode=upcoming-swift)
+
+// REQUIRES: executable_test
+
+import StdlibUnittest
+import StdFunction
+
+var StdFunctionTestSuite = TestSuite("StdFunction")
+
+StdFunctionTestSuite.test("init empty") {
+  let f = FunctionIntToInt()
+  expectTrue(isEmptyFunction(f))
+
+  let copied = f
+  expectTrue(isEmptyFunction(copied))
+}
+
+StdFunctionTestSuite.test("call") {
+  let f = getIdentityFunction()
+  expectEqual(123, f(123))
+}
+
+StdFunctionTestSuite.test("retrieve and pass back as parameter") {
+  let res = invokeFunction(getIdentityFunction(), 456)
+  expectEqual(456, res)
+}
+
+runAllTests()
diff --git a/test/Interop/Cxx/stdlib/use-std-pair-typechecker.swift b/test/Interop/Cxx/stdlib/use-std-pair-typechecker.swift
index c24bc9337d109..7c366c2afc884 100644
--- a/test/Interop/Cxx/stdlib/use-std-pair-typechecker.swift
+++ b/test/Interop/Cxx/stdlib/use-std-pair-typechecker.swift
@@ -1,7 +1,12 @@
-// RUN: %target-typecheck-verify-swift -I %S/Inputs -enable-experimental-cxx-interop
+// RUN: not %target-swift-frontend %s -typecheck -I %S/Inputs -enable-experimental-cxx-interop 2>&1 | %FileCheck %s
 
 import StdPair
 
 let u = HasMethodThatReturnsUnsafePair()
-u.getUnsafePair() // expected-error {{value of type 'HasMethodThatReturnsUnsafePair' has no member 'getUnsafePair'}}
-u.getIteratorPair() // expected-error {{value of type 'HasMethodThatReturnsUnsafePair' has no member 'getIteratorPair'}}
+u.getUnsafePair()
+// CHECK: error: value of type 'HasMethodThatReturnsUnsafePair' has no member 'getUnsafePair'
+// CHECK: note: C++ method 'getUnsafePair' may return an interior pointer
+
+u.getIteratorPair()
+// CHECK: error: value of type 'HasMethodThatReturnsUnsafePair' has no member 'getIteratorPair'
+// CHECK: note: C++ method 'getIteratorPair' may return an interior pointer