diff --git a/include/boost/type_traits/is_complete.hpp b/include/boost/type_traits/is_complete.hpp
index 55dbbbf..af9a1ef 100644
--- a/include/boost/type_traits/is_complete.hpp
+++ b/include/boost/type_traits/is_complete.hpp
@@ -27,6 +27,12 @@
 
 namespace boost {
 
+
+//
+// We will undef this if the trait isn't fully functional:
+//
+#define BOOST_TT_HAS_WORKING_IS_COMPLETE
+
 #if !defined(BOOST_NO_SFINAE_EXPR) && !BOOST_WORKAROUND(BOOST_MSVC, <= 1900)
 
    namespace detail{
@@ -74,6 +80,8 @@ namespace boost {
       template <class T> struct is_complete
          : public integral_constant<bool, true> {};
 
+#undef BOOST_TT_HAS_WORKING_IS_COMPLETE
+
 #endif
 
 } // namespace boost
diff --git a/include/boost/type_traits/is_convertible.hpp b/include/boost/type_traits/is_convertible.hpp
index 058301f..bf648fc 100644
--- a/include/boost/type_traits/is_convertible.hpp
+++ b/include/boost/type_traits/is_convertible.hpp
@@ -489,7 +489,10 @@ struct is_convertible : public integral_constant<bool, ::boost::detail::is_conve
 template <class From, class To>
 struct is_convertible : public integral_constant<bool, BOOST_IS_CONVERTIBLE(From, To)> 
 {
-#ifdef __clang__
+#if BOOST_WORKAROUND(BOOST_MSVC, <= 1900)
+   BOOST_STATIC_ASSERT_MSG(boost::is_complete<From>::value || boost::is_void<From>::value || boost::is_array<From>::value || boost::is_reference<From>::value, "From argument type to is_convertible must be a complete type");
+#endif
+#if defined(__clang__)
    // clang's intrinsic doesn't assert on incomplete types:
    BOOST_STATIC_ASSERT_MSG(boost::is_complete<To>::value || boost::is_void<To>::value || boost::is_array<To>::value, "Destination argument type to is_convertible must be a complete type");
    BOOST_STATIC_ASSERT_MSG(boost::is_complete<From>::value || boost::is_void<From>::value || boost::is_array<From>::value, "From argument type to is_convertible must be a complete type");
diff --git a/test/compile_fail/is_assignable_fail.cpp b/test/compile_fail/is_assignable_fail.cpp
index b745443..2ea6ac2 100644
--- a/test/compile_fail/is_assignable_fail.cpp
+++ b/test/compile_fail/is_assignable_fail.cpp
@@ -7,6 +7,10 @@
 #  include <boost/type_traits/is_assignable.hpp>
 #include "../test.hpp"
 
+#ifndef BOOST_TT_HAS_WORKING_IS_COMPLETE
+#error "Sorry can't test this."
+#endif
+
 int main()
 {
    return boost::is_assignable<incomplete_type>::value;
diff --git a/test/compile_fail/is_convertible2_fail.cpp b/test/compile_fail/is_convertible2_fail.cpp
index 0afd996..8a4a051 100644
--- a/test/compile_fail/is_convertible2_fail.cpp
+++ b/test/compile_fail/is_convertible2_fail.cpp
@@ -7,8 +7,8 @@
 #  include <boost/type_traits/is_convertible.hpp>
 #include "../test.hpp"
 
-#if defined(CI_SUPPRESS_KNOWN_ISSUES) && defined(BOOST_MSVC) && (BOOST_MSVC <= 1800)
-#error "Sorry check doesn't work"
+#ifndef BOOST_TT_HAS_WORKING_IS_COMPLETE
+#error "Sorry can't test this."
 #endif
 
 int main()
diff --git a/test/compile_fail/is_list_constructible_fail.cpp b/test/compile_fail/is_list_constructible_fail.cpp
index 429f8de..eb69bd1 100644
--- a/test/compile_fail/is_list_constructible_fail.cpp
+++ b/test/compile_fail/is_list_constructible_fail.cpp
@@ -7,6 +7,10 @@
 #  include <boost/type_traits/is_list_constructible.hpp>
 #include "../test.hpp"
 
+#ifndef BOOST_TT_HAS_WORKING_IS_COMPLETE
+#error "Sorry can't test this."
+#endif
+
 int main()
 {
    return boost::is_list_constructible<incomplete_type>::value;
diff --git a/test/is_complete_test.cpp b/test/is_complete_test.cpp
index b981f18..075e70d 100644
--- a/test/is_complete_test.cpp
+++ b/test/is_complete_test.cpp
@@ -31,7 +31,7 @@ BOOST_CHECK_INTEGRAL_CONSTANT(::tt::is_complete<int[2]>::value, true);
 BOOST_CHECK_INTEGRAL_CONSTANT(::tt::is_complete<int const[3]>::value, true);
 BOOST_CHECK_INTEGRAL_CONSTANT(::tt::is_complete<int volatile[2][3]>::value, true);
 BOOST_CHECK_INTEGRAL_CONSTANT(::tt::is_complete<int const volatile[4][5][6]>::value, true);
-#ifndef BOOST_NO_SFINAE
+#ifdef BOOST_TT_HAS_WORKING_IS_COMPLETE
 BOOST_CHECK_INTEGRAL_CONSTANT(::tt::is_complete<int[]>::value, false);
 #endif
 
@@ -43,7 +43,7 @@ BOOST_CHECK_INTEGRAL_CONSTANT(::tt::is_complete<cmf>::value, true);
 BOOST_CHECK_INTEGRAL_CONSTANT(::tt::is_complete<mf8>::value, true);
 BOOST_CHECK_INTEGRAL_CONSTANT(::tt::is_complete<union_UDT>::value, true);
 BOOST_CHECK_INTEGRAL_CONSTANT(::tt::is_complete<test_abc1>::value, true);
-#ifndef BOOST_NO_SFINAE
+#ifdef BOOST_TT_HAS_WORKING_IS_COMPLETE
 BOOST_CHECK_INTEGRAL_CONSTANT(::tt::is_complete<incomplete_type>::value, false);
 #endif
 BOOST_CHECK_INTEGRAL_CONSTANT(::tt::is_complete<polymorphic_base>::value, true);