diff --git a/src/vrend_formats.c b/src/vrend_formats.c
index 4647c43..2ecdbb4 100644
--- a/src/vrend_formats.c
+++ b/src/vrend_formats.c
@@ -453,35 +453,47 @@ unsigned vrend_renderer_query_multisample_caps(unsigned max_samples, struct virg
    uint max_samples_confirmed = 1;
    uint test_num_samples[4] = {2,4,8,16};
    int out_buf_offsets[4] = {0,1,2,4};
+   int lowest_working_ms_count_idx = -1;
 
    glGenFramebuffers( 1, &fbo );
    memset(caps->sample_locations, 0, 8 * sizeof(uint32_t));
 
-   for (int i = 0; i < 4 && test_num_samples[i] <= max_samples; ++i) {
+   for (int i = 3; i >= 0; i--) {
+      if (test_num_samples[i] > max_samples)
+         continue;
       glGenTextures(1, &tex);
       glBindTexture(GL_TEXTURE_2D_MULTISAMPLE, tex);
-      glTexStorage2DMultisample(GL_TEXTURE_2D_MULTISAMPLE, test_num_samples[i], GL_RGBA32F, 16, 16, GL_TRUE);
+      glTexStorage2DMultisample(GL_TEXTURE_2D_MULTISAMPLE, test_num_samples[i], GL_RGBA32F, 64, 64, GL_TRUE);
       status = glGetError();
       if (status == GL_NO_ERROR) {
          glBindFramebuffer(GL_FRAMEBUFFER, fbo);
          glFramebufferTexture2D(GL_FRAMEBUFFER, GL_COLOR_ATTACHMENT0, GL_TEXTURE_2D_MULTISAMPLE, tex, 0);
          status = glCheckFramebufferStatus(GL_FRAMEBUFFER);
          if (status == GL_FRAMEBUFFER_COMPLETE) {
-            max_samples_confirmed = test_num_samples[i];
+            if (max_samples_confirmed < test_num_samples[i])
+               max_samples_confirmed = test_num_samples[i];
 
             for (uint k = 0; k < test_num_samples[i]; ++k) {
                float msp[2];
                uint32_t compressed;
                glGetMultisamplefv(GL_SAMPLE_POSITION, k, msp);
-               debug_printf("VIRGL: sample postion [%2d/%2d] = (%f, %f)\n",
-                            k, test_num_samples[i], msp[0], msp[1]);
                compressed = ((unsigned)(floor(msp[0] * 16.0f)) & 0xf) << 4;
                compressed |= ((unsigned)(floor(msp[1] * 16.0f)) & 0xf);
                caps->sample_locations[out_buf_offsets[i] + (k >> 2)] |= compressed  << (8 * (k & 3));
             }
+            lowest_working_ms_count_idx = i;
+         } else {
+            /* If a framebuffer doesn't support low sample counts,
+             * use the sample position from the last working larger count. */
+            if (lowest_working_ms_count_idx > 0) {
+               for (uint k = 0; k < test_num_samples[i]; ++k) {
+                  caps->sample_locations[out_buf_offsets[i] + (k >> 2)] =
+                        caps->sample_locations[out_buf_offsets[lowest_working_ms_count_idx]  + (k >> 2)];
+               }
+            }
          }
+         glBindFramebuffer(GL_FRAMEBUFFER, 0);
       }
-      glBindFramebuffer(GL_FRAMEBUFFER, 0);
       glDeleteTextures(1, &tex);
    }
    glDeleteFramebuffers(1, &fbo);