diff --git a/src/sna/gen4_render.c b/src/sna/gen4_render.c
index 84d78531..3486e086 100644
--- a/src/sna/gen4_render.c
+++ b/src/sna/gen4_render.c
@@ -2478,6 +2478,14 @@ fallback_tiled_dst:
 	if (tmp.redirect.real_bo)
 		kgem_bo_destroy(&sna->kgem, tmp.dst.bo);
 fallback_tiled:
+	if (sna_blt_compare_depth(&src->drawable, &dst->drawable) &&
+	    sna_blt_copy_boxes(sna, alu,
+			       src_bo, src_dx, src_dy,
+			       dst_bo, dst_dx, dst_dy,
+			       dst->drawable.bitsPerPixel,
+			       box, n))
+		return true;
+
 	return sna_tiling_copy_boxes(sna, alu,
 				     src, src_bo, src_dx, src_dy,
 				     dst, dst_bo, dst_dx, dst_dy,
diff --git a/src/sna/gen5_render.c b/src/sna/gen5_render.c
index 34cfd0e0..5b48537e 100644
--- a/src/sna/gen5_render.c
+++ b/src/sna/gen5_render.c
@@ -2443,6 +2443,14 @@ fallback_tiled_dst:
 	if (tmp.redirect.real_bo)
 		kgem_bo_destroy(&sna->kgem, tmp.dst.bo);
 fallback_tiled:
+	if (sna_blt_compare_depth(&src->drawable, &dst->drawable) &&
+	    sna_blt_copy_boxes(sna, alu,
+			       src_bo, src_dx, src_dy,
+			       dst_bo, dst_dx, dst_dy,
+			       dst->drawable.bitsPerPixel,
+			       box, n))
+		return true;
+
 	return sna_tiling_copy_boxes(sna, alu,
 				     src, src_bo, src_dx, src_dy,
 				     dst, dst_bo, dst_dx, dst_dy,
diff --git a/src/sna/gen6_render.c b/src/sna/gen6_render.c
index 0c55a2d0..dd8f0dce 100644
--- a/src/sna/gen6_render.c
+++ b/src/sna/gen6_render.c
@@ -2897,6 +2897,14 @@ fallback_tiled_dst:
 	if (tmp.redirect.real_bo)
 		kgem_bo_destroy(&sna->kgem, tmp.dst.bo);
 fallback_tiled:
+	if (sna_blt_compare_depth(&src->drawable, &dst->drawable) &&
+	    sna_blt_copy_boxes(sna, alu,
+			       src_bo, src_dx, src_dy,
+			       dst_bo, dst_dx, dst_dy,
+			       dst->drawable.bitsPerPixel,
+			       box, n))
+		return true;
+
 	return sna_tiling_copy_boxes(sna, alu,
 				     src, src_bo, src_dx, src_dy,
 				     dst, dst_bo, dst_dx, dst_dy,
diff --git a/src/sna/gen7_render.c b/src/sna/gen7_render.c
index d1ab2e3d..edab5dbc 100644
--- a/src/sna/gen7_render.c
+++ b/src/sna/gen7_render.c
@@ -2990,6 +2990,14 @@ fallback_tiled_dst:
 	if (tmp.redirect.real_bo)
 		kgem_bo_destroy(&sna->kgem, tmp.dst.bo);
 fallback_tiled:
+	if (sna_blt_compare_depth(&src->drawable, &dst->drawable) &&
+	    sna_blt_copy_boxes(sna, alu,
+			       src_bo, src_dx, src_dy,
+			       dst_bo, dst_dx, dst_dy,
+			       dst->drawable.bitsPerPixel,
+			       box, n))
+		return true;
+
 	return sna_tiling_copy_boxes(sna, alu,
 				     src, src_bo, src_dx, src_dy,
 				     dst, dst_bo, dst_dx, dst_dy,