diff --git a/.gitlab-ci/deqp-llvmpipe-fails.txt b/.gitlab-ci/deqp-llvmpipe-fails.txt
index 05da36f575a..795cc4bab44 100644
--- a/.gitlab-ci/deqp-llvmpipe-fails.txt
+++ b/.gitlab-ci/deqp-llvmpipe-fails.txt
@@ -28,7 +28,6 @@ dEQP-GLES2.functional.rasterization.interpolation.basic.lines_wide
 dEQP-GLES2.functional.rasterization.interpolation.projected.line_loop_wide
 dEQP-GLES2.functional.rasterization.interpolation.projected.line_strip_wide
 dEQP-GLES2.functional.rasterization.interpolation.projected.lines_wide
-dEQP-GLES2.functional.rasterization.limits.points
 dEQP-GLES2.functional.shaders.texture_functions.fragment.texture2d_bias
 dEQP-GLES2.functional.shaders.texture_functions.fragment.texture2dproj_vec3_bias
 dEQP-GLES2.functional.shaders.texture_functions.fragment.texture2dproj_vec4_bias
diff --git a/.gitlab-ci/deqp-virgl-fails.txt b/.gitlab-ci/deqp-virgl-fails.txt
index 463ab89eeea..afb05cf55ec 100644
--- a/.gitlab-ci/deqp-virgl-fails.txt
+++ b/.gitlab-ci/deqp-virgl-fails.txt
@@ -30,7 +30,6 @@ dEQP-GLES2.functional.rasterization.interpolation.basic.lines_wide
 dEQP-GLES2.functional.rasterization.interpolation.projected.line_loop_wide
 dEQP-GLES2.functional.rasterization.interpolation.projected.line_strip_wide
 dEQP-GLES2.functional.rasterization.interpolation.projected.lines_wide
-dEQP-GLES2.functional.rasterization.limits.points
 dEQP-GLES3.functional.clipping.line.wide_line_clip_viewport_corner
 dEQP-GLES3.functional.clipping.point.wide_point_clip_viewport_center
 dEQP-GLES3.functional.clipping.triangle_vertex.clip_two.clip_neg_y_neg_z_and_neg_x_neg_y_pos_z
diff --git a/src/gallium/drivers/llvmpipe/lp_limits.h b/src/gallium/drivers/llvmpipe/lp_limits.h
index 569179ecdf4..945156bf0ea 100644
--- a/src/gallium/drivers/llvmpipe/lp_limits.h
+++ b/src/gallium/drivers/llvmpipe/lp_limits.h
@@ -95,4 +95,8 @@
  */
 #define LP_MAX_SETUP_VARIANTS 64
 
+/*
+ * Max point size reported. Cap vertex shader point sizes to this.
+ */
+#define LP_MAX_POINT_WIDTH 255.0f
 #endif /* LP_LIMITS_H */
diff --git a/src/gallium/drivers/llvmpipe/lp_screen.c b/src/gallium/drivers/llvmpipe/lp_screen.c
index 9109e471108..9b691e819b1 100644
--- a/src/gallium/drivers/llvmpipe/lp_screen.c
+++ b/src/gallium/drivers/llvmpipe/lp_screen.c
@@ -478,7 +478,7 @@ llvmpipe_get_paramf(struct pipe_screen *screen, enum pipe_capf param)
    case PIPE_CAPF_MAX_POINT_WIDTH:
       /* fall-through */
    case PIPE_CAPF_MAX_POINT_WIDTH_AA:
-      return 255.0; /* arbitrary */
+      return LP_MAX_POINT_WIDTH; /* arbitrary */
    case PIPE_CAPF_MAX_TEXTURE_ANISOTROPY:
       return 16.0; /* not actually signficant at this time */
    case PIPE_CAPF_MAX_TEXTURE_LOD_BIAS:
diff --git a/src/gallium/drivers/llvmpipe/lp_setup_point.c b/src/gallium/drivers/llvmpipe/lp_setup_point.c
index 092febdba92..fe0de06d15f 100644
--- a/src/gallium/drivers/llvmpipe/lp_setup_point.c
+++ b/src/gallium/drivers/llvmpipe/lp_setup_point.c
@@ -337,10 +337,13 @@ try_setup_point( struct lp_setup_context *setup,
    /* x/y positions in fixed point */
    const struct lp_setup_variant_key *key = &setup->setup.variant->key;
    const int sizeAttr = setup->psize_slot;
-   const float size
+   float size
       = (setup->point_size_per_vertex && sizeAttr > 0) ? v0[sizeAttr][0]
       : setup->point_size;
 
+   if (size > LP_MAX_POINT_WIDTH)
+      size = LP_MAX_POINT_WIDTH;
+
    /* Yes this is necessary to accurately calculate bounding boxes
     * with the two fill-conventions we support.  GL (normally) ends
     * up needing a bottom-left fill convention, which requires