diff --git a/src/freedreno/ci/deqp-freedreno-a530-fails.txt b/src/freedreno/ci/deqp-freedreno-a530-fails.txt
index baa8b6fe709..adc99a8239f 100644
--- a/src/freedreno/ci/deqp-freedreno-a530-fails.txt
+++ b/src/freedreno/ci/deqp-freedreno-a530-fails.txt
@@ -125,20 +125,6 @@ dEQP-GLES31.functional.texture.border_clamp.sampler.uint_stencil,Fail
 dEQP-GLES31.functional.texture.border_clamp.sampler.unorm_depth,Fail
 dEQP-GLES31.functional.texture.border_clamp.unused_channels.r16i,Fail
 dEQP-GLES31.functional.texture.border_clamp.unused_channels.r8,Fail
-dEQP-GLES31.functional.texture.texture_buffer.modify.bufferdata.buffer_size_131071,Fail
-dEQP-GLES31.functional.texture.texture_buffer.modify.bufferdata.range_size_98304,Fail
-dEQP-GLES31.functional.texture.texture_buffer.modify.mapbuffer_write.buffer_size_131071,Fail
-dEQP-GLES31.functional.texture.texture_buffer.modify.mapbuffer_write.range_size_98304,Fail
-dEQP-GLES31.functional.texture.texture_buffer.render.as_fragment_texture.buffer_size_131071,Fail
-dEQP-GLES31.functional.texture.texture_buffer.render.as_fragment_texture.range_size_98304,Fail
-dEQP-GLES31.functional.texture.texture_buffer.render.as_index_array_as_fragment_texture.buffer_size_131071,Fail
-dEQP-GLES31.functional.texture.texture_buffer.render.as_index_array_as_fragment_texture.range_size_98304,Fail
-dEQP-GLES31.functional.texture.texture_buffer.render.as_index_array_as_vertex_texture_as_fragment_texture.buffer_size_131071,Fail
-dEQP-GLES31.functional.texture.texture_buffer.render.as_index_array_as_vertex_texture_as_fragment_texture.range_size_98304,Fail
-dEQP-GLES31.functional.texture.texture_buffer.render.as_vertex_texture_as_fragment_texture.buffer_size_131071,Fail
-dEQP-GLES31.functional.texture.texture_buffer.render.as_vertex_texture_as_fragment_texture.range_size_98304,Fail
-dEQP-GLES31.functional.texture.texture_buffer.state_query.max_texture_buffer_size_getfloat,Fail
-dEQP-GLES31.functional.texture.texture_buffer.state_query.max_texture_buffer_size_getinteger,Fail
 dEQP-GLES3.functional.clipping.line.wide_line_clip_viewport_corner,Fail
 dEQP-GLES3.functional.clipping.point.wide_point_clip_viewport_center,Fail
 dEQP-GLES3.functional.fbo.blit.depth_stencil.depth24_stencil8_scale,Fail
diff --git a/src/gallium/drivers/freedreno/freedreno_screen.c b/src/gallium/drivers/freedreno/freedreno_screen.c
index d00e1e42988..533df75292a 100644
--- a/src/gallium/drivers/freedreno/freedreno_screen.c
+++ b/src/gallium/drivers/freedreno/freedreno_screen.c
@@ -285,8 +285,12 @@ fd_screen_get_param(struct pipe_screen *pscreen, enum pipe_cap param)
 		 */
 		if (is_a3xx(screen)) return 8192;
 		if (is_a4xx(screen)) return 16384;
-		if (is_a5xx(screen)) return 16384;
-		if (is_a6xx(screen)) return 1 << 27;
+
+		/* Note that the Vulkan blob on a540 and 640 report a
+		 * maxTexelBufferElements of just 65536 (the GLES3.2 and Vulkan
+		 * minimum).
+		 */
+		if (is_a5xx(screen) || is_a6xx(screen)) return 1 << 27;
 		return 0;
 
 	case PIPE_CAP_TEXTURE_FLOAT_LINEAR: