diff --git a/src/gallium/drivers/zink/ci/piglit-zink-lvp-fails.txt b/src/gallium/drivers/zink/ci/piglit-zink-lvp-fails.txt
index 876faca1a3a..732e12ce7c7 100644
--- a/src/gallium/drivers/zink/ci/piglit-zink-lvp-fails.txt
+++ b/src/gallium/drivers/zink/ci/piglit-zink-lvp-fails.txt
@@ -48,7 +48,6 @@ spec@!opengl 1.1@read-front clear-front-first samples=2,Fail
 spec@!opengl 1.1@read-front clear-front-first samples=4,Fail
 spec@!opengl 1.1@read-front samples=2,Fail
 spec@!opengl 1.1@read-front samples=4,Fail
-spec@!opengl 1.1@texwrap formats bordercolor-swizzled,Fail
 spec@!opengl 1.2@copyteximage 3d,Fail
 spec@!opengl 1.4@gl-1.4-polygon-offset,Fail
 spec@!opengl 2.0@depth-tex-modes-glsl,Fail
@@ -65,7 +64,6 @@ spec@!opengl 3.2@gl-3.2-adj-prims pv-first,Fail
 spec@!opengl es 2.0@glsl-fs-pointcoord,Fail
 spec@!opengl es 3.0@gles-3.0-transform-feedback-uniform-buffer-object,Fail
 spec@arb_depth_texture@depth-tex-modes,Fail
-spec@arb_es2_compatibility@texwrap formats bordercolor-swizzled,Fail
 spec@arb_fragment_program@fp-abs-01,Crash
 spec@arb_framebuffer_object@fbo-blit-scaled-linear,Fail
 spec@arb_framebuffer_object@fbo-gl_pointcoord,Fail
@@ -92,16 +90,9 @@ spec@arb_tessellation_shader@arb_tessellation_shader-tes-gs-max-output -small -s
 spec@arb_texture_buffer_object@indexed,Fail
 spec@arb_texture_buffer_object@render-no-bo,Crash
 spec@arb_texture_buffer_range@ranges-2 compat,Fail
-spec@arb_texture_compression@texwrap formats bordercolor-swizzled,Fail
-spec@arb_texture_compression_bptc@texwrap formats bordercolor-swizzled,Fail
 spec@arb_texture_cube_map_array@arb_texture_cube_map_array-sampler-cube-array-shadow,Fail
 spec@arb_texture_float@fbo-blending-formats,Fail
-spec@arb_texture_float@texwrap formats bordercolor-swizzled,Fail
 spec@arb_texture_rg@multisample-fast-clear gl_arb_texture_rg-int,Fail
-spec@arb_texture_rg@texwrap formats bordercolor-swizzled,Fail
-spec@arb_texture_rg@texwrap formats-float bordercolor-swizzled,Fail
-spec@arb_texture_rg@texwrap formats-int bordercolor-swizzled,Fail
-spec@arb_texture_rgb10_a2ui@texwrap formats bordercolor-swizzled,Fail
 spec@arb_texture_view@rendering-formats,Fail
 spec@arb_texture_view@sampling-2d-array-as-cubemap-array,Fail
 spec@arb_uniform_buffer_object@maxblocks,Crash
@@ -171,16 +162,8 @@ spec@ext_image_dma_buf_import@ext_image_dma_buf_import-sample_yvu420,Fail
 spec@ext_image_dma_buf_import@ext_image_dma_buf_import-transcode-nv12-as-r8-gr88,Fail
 spec@ext_image_dma_buf_import@ext_image_dma_buf_import-unsupported_format,Fail
 spec@ext_packed_float@query-rgba-signed-components,Fail
-spec@ext_packed_float@texwrap formats bordercolor-swizzled,Fail
-spec@ext_texture_compression_rgtc@texwrap formats bordercolor-swizzled,Fail
-spec@ext_texture_compression_s3tc@texwrap formats bordercolor-swizzled,Fail
 spec@ext_texture_integer@multisample-fast-clear gl_ext_texture_integer,Fail
-spec@ext_texture_integer@texwrap formats bordercolor-swizzled,Fail
-spec@ext_texture_shared_exponent@texwrap formats bordercolor-swizzled,Fail
 spec@ext_texture_snorm@fbo-blending-formats,Fail
-spec@ext_texture_snorm@texwrap formats bordercolor-swizzled,Fail
-spec@ext_texture_srgb@texwrap formats bordercolor-swizzled,Fail
-spec@ext_texture_srgb@texwrap formats-s3tc bordercolor-swizzled,Fail
 spec@ext_texture_swizzle@depth_texture_mode_and_swizzle,Fail
 spec@ext_transform_feedback2@counting with pause,Fail
 spec@ext_transform_feedback@generatemipmap prims_generated,Fail
diff --git a/src/gallium/drivers/zink/zink_screen.c b/src/gallium/drivers/zink/zink_screen.c
index c0ad728c2e7..8137d38d18c 100644
--- a/src/gallium/drivers/zink/zink_screen.c
+++ b/src/gallium/drivers/zink/zink_screen.c
@@ -324,9 +324,13 @@ zink_get_param(struct pipe_screen *pscreen, enum pipe_cap param)
       return 0;
 
    case PIPE_CAP_TEXTURE_BORDER_COLOR_QUIRK:
-      return screen->info.driver_props.driverID == VK_DRIVER_ID_INTEL_OPEN_SOURCE_MESA_KHR ||
-             screen->info.driver_props.driverID == VK_DRIVER_ID_INTEL_PROPRIETARY_WINDOWS_KHR ?
-             0 : PIPE_QUIRK_TEXTURE_BORDER_COLOR_SWIZZLE_NV50;
+      /* This is also broken on the other AMD drivers for old HW, but
+       * there's no obvious way to test for that.
+       */
+      if (screen->info.driver_props.driverID == VK_DRIVER_ID_MESA_RADV ||
+          screen->info.driver_props.driverID == VK_DRIVER_ID_NVIDIA_PROPRIETARY)
+         return PIPE_QUIRK_TEXTURE_BORDER_COLOR_SWIZZLE_NV50;
+      return 0;
 
    case PIPE_CAP_MAX_TEXTURE_2D_SIZE:
       return screen->info.props.limits.maxImageDimension2D;