diff --git a/src/gallium/drivers/llvmpipe/ci/deqp-llvmpipe-fails.txt b/src/gallium/drivers/llvmpipe/ci/deqp-llvmpipe-fails.txt
index 525d25f2aeb..952e45dbd21 100644
--- a/src/gallium/drivers/llvmpipe/ci/deqp-llvmpipe-fails.txt
+++ b/src/gallium/drivers/llvmpipe/ci/deqp-llvmpipe-fails.txt
@@ -47,8 +47,6 @@ dEQP-GLES3.functional.polygon_offset.fixed16_render_with_units,Fail
 dEQP-GLES3.functional.polygon_offset.fixed24_displacement_with_units,Fail
 dEQP-GLES3.functional.polygon_offset.fixed24_render_with_units,Fail
 dEQP-GLES3.functional.polygon_offset.float32_displacement_with_units,Fail
-dEQP-GLES3.functional.rasterization.fbo.rbo_multisample_4.primitives.points,Fail
-dEQP-GLES3.functional.rasterization.fbo.rbo_multisample_max.primitives.points,Fail
 dEQP-GLES3.functional.rasterization.fbo.rbo_singlesample.interpolation.lines_wide,Fail
 dEQP-GLES3.functional.rasterization.fbo.texture_2d.interpolation.lines_wide,Fail
 dEQP-GLES3.functional.rasterization.interpolation.basic.line_loop_wide,Fail
diff --git a/src/gallium/drivers/llvmpipe/lp_setup_point.c b/src/gallium/drivers/llvmpipe/lp_setup_point.c
index 66e1416abeb..bca2d47d135 100644
--- a/src/gallium/drivers/llvmpipe/lp_setup_point.c
+++ b/src/gallium/drivers/llvmpipe/lp_setup_point.c
@@ -355,6 +355,7 @@ try_setup_point( struct lp_setup_context *setup,
    struct lp_rast_triangle *point;
    unsigned bytes;
    struct u_rect bbox;
+   int x[2], y[2];
    unsigned nr_planes = 4;
    struct point_info info;
    unsigned viewport_index = 0;
@@ -374,7 +375,7 @@ try_setup_point( struct lp_setup_context *setup,
       print_point(setup, v0, size);
 
    /* Bounding rectangle (in pixels) */
-   if (!setup->legacy_points) {
+   if (!setup->legacy_points || setup->multisample) {
       /*
        * Rasterize points as quads.
        */
@@ -387,10 +388,14 @@ try_setup_point( struct lp_setup_context *setup,
       x0 = subpixel_snap(v0[0][0] - pixel_offset) - fixed_width/2;
       y0 = subpixel_snap(v0[0][1] - pixel_offset) - fixed_width/2;
 
-      bbox.x0 = (x0 + (FIXED_ONE-1)) >> FIXED_ORDER;
-      bbox.x1 = (x0 + fixed_width + (FIXED_ONE-1)) >> FIXED_ORDER;
-      bbox.y0 = (y0 + (FIXED_ONE-1) + adj) >> FIXED_ORDER;
-      bbox.y1 = (y0 + fixed_width + (FIXED_ONE-1) + adj) >> FIXED_ORDER;
+      x[0] = x0;
+      x[1] = x0 + fixed_width;
+      y[0] = y0;
+      y[1] = y0 + fixed_width;
+      bbox.x0 = x[0] >> FIXED_ORDER;
+      bbox.x1 = (x[1] + (FIXED_ONE-1)) >> FIXED_ORDER;
+      bbox.y0 = (y[0] + adj) >> FIXED_ORDER;
+      bbox.y1 = (y[1] + (FIXED_ONE-1) + adj) >> FIXED_ORDER;
 
       /* Inclusive coordinates:
        */
@@ -438,6 +443,11 @@ try_setup_point( struct lp_setup_context *setup,
          bbox.x1 = bbox.x0 + int_width - 1;
          bbox.y1 = bbox.y0 + int_width - 1;
       }
+
+      x[0] = (bbox.x0 - 1) << 8;
+      x[1] = (bbox.x1 + 1) << 8;
+      y[0] = (bbox.y0 - 1) << 8;
+      y[1] = (bbox.y1 + 1) << 8;
    }
 
    if (0) {
@@ -504,23 +514,32 @@ try_setup_point( struct lp_setup_context *setup,
 
       plane[0].dcdx = ~0U << 8;
       plane[0].dcdy = 0;
-      plane[0].c = (1-bbox.x0) << 8;
+      plane[0].c = -x[0];
       plane[0].eo = 1 << 8;
 
       plane[1].dcdx = 1 << 8;
       plane[1].dcdy = 0;
-      plane[1].c = (bbox.x1+1) << 8;
+      plane[1].c = x[1];
       plane[1].eo = 0;
 
       plane[2].dcdx = 0;
       plane[2].dcdy = 1 << 8;
-      plane[2].c = (1-bbox.y0) << 8;
+      plane[2].c = -y[0];
       plane[2].eo = 1 << 8;
 
       plane[3].dcdx = 0;
       plane[3].dcdy = ~0U << 8;
-      plane[3].c = (bbox.y1+1) << 8;
+      plane[3].c = y[1];
       plane[3].eo = 0;
+
+      if (!setup->legacy_points || setup->multisample) {
+         /* adjust for fill-rule*/
+         plane[0].c++; /* left */
+         if (setup->bottom_edge_rule == 0)
+            plane[2].c++; /* top-left */
+         else
+            plane[3].c++; /* bottom-left */
+      }
    }
 
    return lp_setup_bin_triangle(setup, point, &bbox, &bbox, nr_planes, viewport_index);
diff --git a/src/gallium/drivers/virgl/ci/deqp-virgl-gl-fails.txt b/src/gallium/drivers/virgl/ci/deqp-virgl-gl-fails.txt
index b4de9d91f01..38f1a950f98 100644
--- a/src/gallium/drivers/virgl/ci/deqp-virgl-gl-fails.txt
+++ b/src/gallium/drivers/virgl/ci/deqp-virgl-gl-fails.txt
@@ -38,8 +38,6 @@ dEQP-GLES3.functional.polygon_offset.fixed16_render_with_units,Fail
 dEQP-GLES3.functional.polygon_offset.fixed24_displacement_with_units,Fail
 dEQP-GLES3.functional.polygon_offset.fixed24_render_with_units,Fail
 dEQP-GLES3.functional.polygon_offset.float32_displacement_with_units,Fail
-dEQP-GLES3.functional.rasterization.fbo.rbo_multisample_4.primitives.points,Fail
-dEQP-GLES3.functional.rasterization.fbo.rbo_multisample_max.primitives.points,Fail
 dEQP-GLES3.functional.rasterization.fbo.rbo_singlesample.interpolation.lines_wide,Fail
 dEQP-GLES3.functional.rasterization.fbo.texture_2d.interpolation.lines_wide,Fail
 dEQP-GLES3.functional.rasterization.interpolation.basic.line_loop_wide,Fail
diff --git a/src/gallium/drivers/virgl/ci/deqp-virgl-gles-fails.txt b/src/gallium/drivers/virgl/ci/deqp-virgl-gles-fails.txt
index 5b7bafcda0a..63014852eac 100644
--- a/src/gallium/drivers/virgl/ci/deqp-virgl-gles-fails.txt
+++ b/src/gallium/drivers/virgl/ci/deqp-virgl-gles-fails.txt
@@ -37,8 +37,6 @@ dEQP-GLES3.functional.polygon_offset.fixed16_render_with_units,Fail
 dEQP-GLES3.functional.polygon_offset.fixed24_displacement_with_units,Fail
 dEQP-GLES3.functional.polygon_offset.fixed24_render_with_units,Fail
 dEQP-GLES3.functional.polygon_offset.float32_displacement_with_units,Fail
-dEQP-GLES3.functional.rasterization.fbo.rbo_multisample_4.primitives.points,Fail
-dEQP-GLES3.functional.rasterization.fbo.rbo_multisample_max.primitives.points,Fail
 dEQP-GLES3.functional.rasterization.fbo.rbo_singlesample.interpolation.lines_wide,Fail
 dEQP-GLES3.functional.rasterization.fbo.texture_2d.interpolation.lines_wide,Fail
 dEQP-GLES3.functional.rasterization.interpolation.basic.line_loop_wide,Fail
diff --git a/src/gallium/frontends/lavapipe/ci/deqp-lvp-fails.txt b/src/gallium/frontends/lavapipe/ci/deqp-lvp-fails.txt
index a0e6c548572..ccb249844b8 100644
--- a/src/gallium/frontends/lavapipe/ci/deqp-lvp-fails.txt
+++ b/src/gallium/frontends/lavapipe/ci/deqp-lvp-fails.txt
@@ -33,7 +33,6 @@ dEQP-VK.image.mismatched_formats.image_write.a8b8g8r8_srgb_pack32_with_rgb10a2,C
 dEQP-VK.image.mismatched_formats.image_write.b8g8r8a8_srgb_with_rgba8,Crash
 dEQP-VK.image.mismatched_formats.image_write.r8g8b8a8_srgb_with_rgb10a2,Crash
 dEQP-VK.rasterization.interpolation.projected.non_strict_lines,Fail
-dEQP-VK.rasterization.primitives_multisample_4_bit.no_stipple.points,Fail
 dEQP-VK.texture.filtering.2d.combinations.linear_mipmap_linear.linear.clamp_to_edge.repeat,Fail
 dEQP-VK.texture.filtering.2d.combinations.linear_mipmap_linear.linear.mirror_clamp_to_edge.repeat,Fail
 dEQP-VK.texture.filtering.2d.combinations.linear_mipmap_linear.linear.mirrored_repeat.mirror_clamp_to_edge,Fail