diff --git a/glamor/glamor_copyarea.c b/glamor/glamor_copyarea.c
index a39c97001..f2d710a90 100644
--- a/glamor/glamor_copyarea.c
+++ b/glamor/glamor_copyarea.c
@@ -226,6 +226,12 @@ glamor_copy_n_to_n_textured(DrawablePtr src,
 		dispatch->glTexParameteri(GL_TEXTURE_2D,
 					  GL_TEXTURE_MAG_FILTER,
 					  GL_NEAREST);
+		dispatch->glTexParameteri(GL_TEXTURE_2D,
+					  GL_TEXTURE_WRAP_S,
+					  GL_CLAMP_TO_BORDER);
+		dispatch->glTexParameteri(GL_TEXTURE_2D,
+					  GL_TEXTURE_WRAP_T,
+					  GL_CLAMP_TO_BORDER);
 
 		dispatch->glVertexAttribPointer(GLAMOR_VERTEX_SOURCE, 2,
 						GL_FLOAT, GL_FALSE,
diff --git a/glamor/glamor_render.c b/glamor/glamor_render.c
index 1e68e652b..789c684c2 100644
--- a/glamor/glamor_render.c
+++ b/glamor/glamor_render.c
@@ -622,19 +622,21 @@ glamor_composite_with_copy(CARD8 op,
 				      x_source, y_source,
 				      0, 0, x_dest, y_dest, width, height))
 		return TRUE;
-	/* Fallback if we sample outside the source so that we swizzle the
-	 * clear color appropriately. If the source has an alpha channel,
-	 * we could rely on CLAMP_TO_BORDER working as required...
-	 */
-	if (region.extents.x1 + x_source - x_dest < 0)
-		goto cleanup_region;
-	if (region.extents.x2 + x_source - x_dest > source->pDrawable->width)
-		goto cleanup_region;
 
-	if (region.extents.y1 + y_source - y_dest < 0)
-		goto cleanup_region;
-	if (region.extents.y2 + y_source - y_dest > source->pDrawable->height)
-		goto cleanup_region;
+	if (PICT_FORMAT_A(source->format) == 0) {
+		/* Fallback if we sample outside the source so that we
+		 * swizzle the correct clear color for out-of-bounds texels.
+		 */
+		if (region.extents.x1 + x_source - x_dest < 0)
+			goto cleanup_region;
+		if (region.extents.x2 + x_source - x_dest > source->pDrawable->width)
+			goto cleanup_region;
+
+		if (region.extents.y1 + y_source - y_dest < 0)
+			goto cleanup_region;
+		if (region.extents.y2 + y_source - y_dest > source->pDrawable->height)
+			goto cleanup_region;
+	}
 
 	ret = glamor_copy_n_to_n_nf(source->pDrawable,
 				    dest->pDrawable, NULL,