diff --git a/test/Jamfile b/test/Jamfile
index a451e8a..da3d38c 100644
--- a/test/Jamfile
+++ b/test/Jamfile
@@ -41,3 +41,8 @@ run invoke_fn_noexcept_test.cpp ;
 run invoke_obj_noexcept_test.cpp ;
 run invoke_mfn_noexcept_test.cpp ;
 run invoke_md_noexcept_test.cpp ;
+
+compile invoke_fn_constexpr_test.cpp ;
+compile invoke_obj_constexpr_test.cpp ;
+compile invoke_mfn_constexpr_test.cpp ;
+compile invoke_md_constexpr_test.cpp ;
diff --git a/test/invoke_fn_constexpr_test.cpp b/test/invoke_fn_constexpr_test.cpp
new file mode 100644
index 0000000..95f56ff
--- /dev/null
+++ b/test/invoke_fn_constexpr_test.cpp
@@ -0,0 +1,40 @@
+// Copyright 2024 Peter Dimov
+// Distributed under the Boost Software License, Version 1.0.
+// https://www.boost.org/LICENSE_1_0.txt
+
+#if defined(__GNUC__) && __GNUC__ == 7
+# pragma GCC diagnostic ignored "-Wnoexcept-type"
+#endif
+
+#include <boost/compat/invoke.hpp>
+
+#define STATIC_ASSERT(...) static_assert(__VA_ARGS__, #__VA_ARGS__)
+#define BOOST_TEST_EQ(x, y) STATIC_ASSERT((x) == (y))
+
+constexpr int f0()
+{
+    return -1;
+}
+
+constexpr int f1( int x1 ) noexcept
+{
+    return x1;
+}
+
+constexpr int f2( int x1, int x2 )
+{
+    return 10*x1+x2;
+}
+
+constexpr int f3( int x1, int x2, int x3 ) noexcept
+{
+    return 100*x1 + 10*x2 + x3;
+}
+
+int main()
+{
+    BOOST_TEST_EQ( boost::compat::invoke( f0 ), -1 );
+    BOOST_TEST_EQ( boost::compat::invoke( f1, 1 ), 1 );
+    BOOST_TEST_EQ( boost::compat::invoke( f2, 1, 2 ), 12 );
+    BOOST_TEST_EQ( boost::compat::invoke( f3, 1, 2, 3 ), 123 );
+}
diff --git a/test/invoke_md_constexpr_test.cpp b/test/invoke_md_constexpr_test.cpp
new file mode 100644
index 0000000..9f8013e
--- /dev/null
+++ b/test/invoke_md_constexpr_test.cpp
@@ -0,0 +1,43 @@
+// Copyright 2024 Peter Dimov
+// Distributed under the Boost Software License, Version 1.0.
+// https://www.boost.org/LICENSE_1_0.txt
+
+#include <boost/compat/invoke.hpp>
+#include <boost/config.hpp>
+#include <boost/config/workaround.hpp>
+#include <functional>
+
+#define STATIC_ASSERT(...) static_assert(__VA_ARGS__, #__VA_ARGS__)
+#define BOOST_TEST_EQ(x, y) STATIC_ASSERT((x) == (y))
+
+struct X
+{
+    int m = -1;
+};
+
+struct Y: public X
+{
+};
+
+int main()
+{
+    {
+        BOOST_TEST_EQ( boost::compat::invoke( &X::m, X() ), -1 );
+
+        constexpr X x = {};
+
+        BOOST_TEST_EQ( boost::compat::invoke( &X::m, x ), -1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::m, &x ), -1 );
+    }
+
+#if !BOOST_WORKAROUND(BOOST_MSVC, >= 1920 && BOOST_MSVC < 1940)
+    {
+        BOOST_TEST_EQ( boost::compat::invoke( &X::m, Y() ), -1 );
+
+        constexpr Y y = {};
+
+        BOOST_TEST_EQ( boost::compat::invoke( &X::m, y ), -1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::m, &y ), -1 );
+    }
+#endif
+}
diff --git a/test/invoke_mfn_constexpr_test.cpp b/test/invoke_mfn_constexpr_test.cpp
new file mode 100644
index 0000000..62c2b22
--- /dev/null
+++ b/test/invoke_mfn_constexpr_test.cpp
@@ -0,0 +1,89 @@
+// Copyright 2024 Peter Dimov
+// Distributed under the Boost Software License, Version 1.0.
+// https://www.boost.org/LICENSE_1_0.txt
+
+#if defined(__GNUC__) && __GNUC__ == 7
+# pragma GCC diagnostic ignored "-Wnoexcept-type"
+#endif
+
+#include <boost/compat/invoke.hpp>
+#include <boost/config.hpp>
+#include <boost/config/workaround.hpp>
+#include <functional>
+
+#define STATIC_ASSERT(...) static_assert(__VA_ARGS__, #__VA_ARGS__)
+#define BOOST_TEST_EQ(x, y) STATIC_ASSERT((x) == (y))
+
+struct X
+{
+    constexpr int f0() const
+    {
+        return -1;
+    }
+
+    constexpr int f1( int x1 ) const noexcept
+    {
+        return x1;
+    }
+
+    constexpr int f2( int x1, int x2 ) const
+    {
+        return 10*x1+x2;
+    }
+
+    constexpr int f3( int x1, int x2, int x3 ) const noexcept
+    {
+        return 100*x1 + 10*x2 + x3;
+    }
+};
+
+struct Y: public X
+{
+};
+
+int main()
+{
+    {
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f0, X() ), -1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f1, X(), 1 ), 1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f2, X(), 1, 2 ), 12 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f3, X(), 1, 2, 3 ), 123 );
+    }
+
+    {
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f0, Y() ), -1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f1, Y(), 1 ), 1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f2, Y(), 1, 2 ), 12 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f3, Y(), 1, 2, 3 ), 123 );
+    }
+
+    {
+        constexpr X x = {};
+
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f0, x ), -1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f1, x, 1 ), 1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f2, x, 1, 2 ), 12 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f3, x, 1, 2, 3 ), 123 );
+
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f0, &x ), -1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f1, &x, 1 ), 1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f2, &x, 1, 2 ), 12 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f3, &x, 1, 2, 3 ), 123 );
+    }
+
+#if !BOOST_WORKAROUND(BOOST_MSVC, < 1910)
+    {
+        constexpr Y y = {};
+
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f0, y ), -1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f1, y, 1 ), 1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f2, y, 1, 2 ), 12 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f3, y, 1, 2, 3 ), 123 );
+
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f0, &y ), -1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f1, &y, 1 ), 1 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f2, &y, 1, 2 ), 12 );
+        BOOST_TEST_EQ( boost::compat::invoke( &X::f3, &y, 1, 2, 3 ), 123 );
+    }
+#endif
+}
diff --git a/test/invoke_obj_constexpr_test.cpp b/test/invoke_obj_constexpr_test.cpp
new file mode 100644
index 0000000..26368ec
--- /dev/null
+++ b/test/invoke_obj_constexpr_test.cpp
@@ -0,0 +1,50 @@
+// Copyright 2024 Peter Dimov
+// Distributed under the Boost Software License, Version 1.0.
+// https://www.boost.org/LICENSE_1_0.txt
+
+#include <boost/compat/invoke.hpp>
+
+#define STATIC_ASSERT(...) static_assert(__VA_ARGS__, #__VA_ARGS__)
+#define BOOST_TEST_EQ(x, y) STATIC_ASSERT((x) == (y))
+
+struct F
+{
+    constexpr int operator()() const
+    {
+        return -1;
+    }
+
+    constexpr int operator()( int x1 ) const noexcept
+    {
+        return x1;
+    }
+
+    constexpr int operator()( int x1, int x2 ) const
+    {
+        return 10*x1+x2;
+    }
+
+    constexpr int operator()( int x1, int x2, int x3 ) const noexcept
+    {
+        return 100*x1 + 10*x2 + x3;
+    }
+};
+
+int main()
+{
+    {
+        BOOST_TEST_EQ( boost::compat::invoke( F() ), -1 );
+        BOOST_TEST_EQ( boost::compat::invoke( F(), 1 ), 1 );
+        BOOST_TEST_EQ( boost::compat::invoke( F(), 1, 2 ), 12 );
+        BOOST_TEST_EQ( boost::compat::invoke( F(), 1, 2, 3 ), 123 );
+    }
+
+    {
+        constexpr F f = {};
+
+        BOOST_TEST_EQ( boost::compat::invoke( f ), -1 );
+        BOOST_TEST_EQ( boost::compat::invoke( f, 1 ), 1 );
+        BOOST_TEST_EQ( boost::compat::invoke( f, 1, 2 ), 12 );
+        BOOST_TEST_EQ( boost::compat::invoke( f, 1, 2, 3 ), 123 );
+    }
+}