diff --git a/src/glx/clientinfo.c b/src/glx/clientinfo.c
index 8f3fdeba4aa..aed2619888e 100644
--- a/src/glx/clientinfo.c
+++ b/src/glx/clientinfo.c
@@ -39,11 +39,56 @@ __glX_send_client_info(struct glx_display *glx_dpy)
    Bool any_screen_has_ARB_create_context = False;
    Bool any_screen_has_ARB_create_context_profile = False;
    unsigned i;
+   /* You need GLX_ARB_create_context_profile to get beyond 3.1 anyway */
    static const uint32_t gl_versions[] = {
-      1, 4,
+      2, 1,
+      3, 0,
+      3, 1,
    };
+   /*
+    * This is weird, but it matches what NVIDIA does/expects. For big-GL
+    * below 3.2 there is no such thing as a "profile", so we name them all
+    * with no profile bits. Except we don't name anything lower than 2.1,
+    * since GLX_ARB_create_context_profile says:
+    *
+    *   "Only the highest supported version below 3.0 should be sent, since
+    *   OpenGL 2.1 is backwards compatible with all earlier versions."
+    *
+    * In order to also support GLES below 3.2, we name every possible GLES
+    * version with the ES2 bit set, which happens to just mean GLES generally
+    * and not a particular major version. 3.2 happens to be a legal version
+    * number for both big-GL and GLES, so it gets all three bits set.
+    * Everything 3.3 and above is big-GL only so gets the core and compat
+    * bits set.
+    */
    static const uint32_t gl_versions_profiles[] = {
-      1, 4, 0x00000000,
+      1, 0, GLX_CONTEXT_ES2_PROFILE_BIT_EXT,
+      1, 1, GLX_CONTEXT_ES2_PROFILE_BIT_EXT,
+      2, 0, GLX_CONTEXT_ES2_PROFILE_BIT_EXT,
+      2, 1, 0x0,
+      3, 0, 0x0,
+      3, 0, GLX_CONTEXT_ES2_PROFILE_BIT_EXT,
+      3, 1, 0x0,
+      3, 1, GLX_CONTEXT_ES2_PROFILE_BIT_EXT,
+      3, 2, GLX_CONTEXT_CORE_PROFILE_BIT_ARB |
+            GLX_CONTEXT_COMPATIBILITY_PROFILE_BIT_ARB |
+            GLX_CONTEXT_ES2_PROFILE_BIT_EXT,
+      3, 3, GLX_CONTEXT_CORE_PROFILE_BIT_ARB |
+            GLX_CONTEXT_COMPATIBILITY_PROFILE_BIT_ARB,
+      4, 0, GLX_CONTEXT_CORE_PROFILE_BIT_ARB |
+            GLX_CONTEXT_COMPATIBILITY_PROFILE_BIT_ARB,
+      4, 1, GLX_CONTEXT_CORE_PROFILE_BIT_ARB |
+            GLX_CONTEXT_COMPATIBILITY_PROFILE_BIT_ARB,
+      4, 2, GLX_CONTEXT_CORE_PROFILE_BIT_ARB |
+            GLX_CONTEXT_COMPATIBILITY_PROFILE_BIT_ARB,
+      4, 3, GLX_CONTEXT_CORE_PROFILE_BIT_ARB |
+            GLX_CONTEXT_COMPATIBILITY_PROFILE_BIT_ARB,
+      4, 4, GLX_CONTEXT_CORE_PROFILE_BIT_ARB |
+            GLX_CONTEXT_COMPATIBILITY_PROFILE_BIT_ARB,
+      4, 5, GLX_CONTEXT_CORE_PROFILE_BIT_ARB |
+            GLX_CONTEXT_COMPATIBILITY_PROFILE_BIT_ARB,
+      4, 6, GLX_CONTEXT_CORE_PROFILE_BIT_ARB |
+            GLX_CONTEXT_COMPATIBILITY_PROFILE_BIT_ARB,
    };
    static const char glx_extensions[] =
       "GLX_ARB_create_context GLX_ARB_create_context_profile";
@@ -70,8 +115,6 @@ __glX_send_client_info(struct glx_display *glx_dpy)
     * imagine an implementation that supports GLX_SGIX_fbconfig and
     * GLX_ARB_create_context but not GLX 1.4.  Making GLX 1.4 a hard
     * requirement in this case does not seem like a limitation.
-    *
-    * This library currently only supports struct GLXClientInfo.
     */
 
    if (glx_dpy->majorVersion == 1 && glx_dpy->minorVersion == 0)
diff --git a/src/glx/tests/clientinfo_unittest.cpp b/src/glx/tests/clientinfo_unittest.cpp
index 320e8fcc0ac..56892769114 100644
--- a/src/glx/tests/clientinfo_unittest.cpp
+++ b/src/glx/tests/clientinfo_unittest.cpp
@@ -576,6 +576,7 @@ TEST_F(glX_send_client_info_test, gl_versions_and_profiles_are_sane)
 
    const uint32_t all_valid_bits = GLX_CONTEXT_CORE_PROFILE_BIT_ARB
       | GLX_CONTEXT_COMPATIBILITY_PROFILE_BIT_ARB;
+   const uint32_t es_bit = GLX_CONTEXT_ES2_PROFILE_BIT_EXT;
 
    unsigned versions_below_3_0 = 0;
 
@@ -588,14 +589,24 @@ TEST_F(glX_send_client_info_test, gl_versions_and_profiles_are_sane)
        */
       switch (gl_versions[i * 3]) {
       case 1:
-	 EXPECT_GE(5u, gl_versions[i * 3 + 1]);
-	 EXPECT_EQ(0u, gl_versions[i * 3 + 2]);
-	 versions_below_3_0++;
+         if (gl_versions[i * 3 + 2] & es_bit) {
+            EXPECT_GE(1u, gl_versions[i * 3 + 1]);
+            EXPECT_EQ(es_bit, gl_versions[i * 3 + 2]);
+         } else {
+            EXPECT_GE(5u, gl_versions[i * 3 + 1]);
+            EXPECT_EQ(0u, gl_versions[i * 3 + 2]);
+            versions_below_3_0++;
+         }
 	 break;
       case 2:
-	 EXPECT_GE(1u, gl_versions[i * 3 + 1]);
-	 EXPECT_EQ(0u, gl_versions[i * 3 + 2]);
-	 versions_below_3_0++;
+         if (gl_versions[i * 3 + 2] & es_bit) {
+            EXPECT_EQ(0u, gl_versions[i * 3 + 1]);
+            EXPECT_EQ(es_bit, gl_versions[i * 3 + 2]);
+         } else {
+            EXPECT_GE(1u, gl_versions[i * 3 + 1]);
+            EXPECT_EQ(0u, gl_versions[i * 3 + 2]);
+            versions_below_3_0++;
+         }
 	 break;
       case 3:
 	 EXPECT_GE(3u, gl_versions[i * 3 + 1]);
@@ -603,14 +614,16 @@ TEST_F(glX_send_client_info_test, gl_versions_and_profiles_are_sane)
 	 /* Profiles were not introduced until OpenGL 3.2.
 	  */
 	 if (gl_versions[i * 3 + 1] < 2) {
-	    EXPECT_EQ(0u, gl_versions[i * 3 + 2]);
+	    EXPECT_EQ(0u, gl_versions[i * 3 + 2] & ~(es_bit));
+	 } else if (gl_versions[i * 3 + 1] == 2) {
+	    EXPECT_EQ(0u, gl_versions[i * 3 + 2] & ~(all_valid_bits | es_bit));
 	 } else {
-	    EXPECT_EQ(0u, gl_versions[i * 3 + 2] & ~all_valid_bits);
-	 }
+	    EXPECT_EQ(0u, gl_versions[i * 3 + 2] & ~(all_valid_bits));
+         }
 	 break;
       case 4:
-	 EXPECT_GE(2u, gl_versions[i * 3 + 1]);
-	 EXPECT_EQ(0u, gl_versions[i * 3 + 2] & ~all_valid_bits);
+	 EXPECT_GE(6u, gl_versions[i * 3 + 1]);
+	 EXPECT_EQ(0u, gl_versions[i * 3 + 2] & ~(all_valid_bits));
 	 break;
       }
    }