diff --git a/src/cairo-xcb-surface-render.c b/src/cairo-xcb-surface-render.c
index 6f29224..efbf648 100644
--- a/src/cairo-xcb-surface-render.c
+++ b/src/cairo-xcb-surface-render.c
@@ -4514,7 +4514,6 @@ _composite_glyphs (void				*closure,
 	 */
 	this_x = _cairo_lround (info->glyphs[i].d.x) - dst_x;
 	this_y = _cairo_lround (info->glyphs[i].d.y) - dst_y;
-	assert (! (((this_x+4096) | (this_y+4096)) & ~0x3fffu));
 
 	this_glyphset_info = _cairo_xcb_scaled_glyph_get_glyphset_info (scaled_glyph);
 	if (glyphset_info == NULL)
@@ -4542,7 +4541,9 @@ _composite_glyphs (void				*closure,
 	 * to the mask first, and then composes that to final surface,
 	 * though it's not a big deal.
 	 */
-	if (request_size + width > max_request_size - _cairo_sz_x_glyph_elt_t ||
+	if ((this_x - x) > INT16_MAX || (this_x - x) < INT16_MIN ||
+	    (this_y - y) > INT16_MAX || (this_y - y) < INT16_MIN ||
+	    request_size + width > max_request_size - _cairo_sz_x_glyph_elt_t ||
 	    this_glyphset_info != glyphset_info)
 	{
 	    status = _emit_glyphs_chunk (dst, op, src,
diff --git a/src/cairo-xlib-surface.c b/src/cairo-xlib-surface.c
index 6d593c0..11bcec7 100644
--- a/src/cairo-xlib-surface.c
+++ b/src/cairo-xlib-surface.c
@@ -4556,9 +4556,6 @@ _cairo_xlib_surface_emit_glyphs (cairo_xlib_display_t *display,
 	 * Update: upon seeing weird glyphs, we just return and let fallback
 	 * code do the job.
 	 */
-	if (((this_x+4096)|(this_y+4096))&~0x3fffu)
-	    break;
-
 	/* Send unsent glyphs to the server */
 	if (_cairo_xlib_scaled_glyph_get_glyphset_info (scaled_glyph) == NULL) {
 	    status = _cairo_xlib_surface_add_glyph (display,
@@ -4606,7 +4603,9 @@ _cairo_xlib_surface_emit_glyphs (cairo_xlib_display_t *display,
 	 * to the mask first, and then composes that to final surface,
 	 * though it's not a big deal.
 	 */
-	if (request_size + width > max_request_size - _cairo_sz_xGlyphElt ||
+	if ((this_x - x) > INT16_MAX || (this_x - x) < INT16_MIN ||
+	    (this_y - y) > INT16_MAX || (this_y - y) < INT16_MIN ||
+	    request_size + width > max_request_size - _cairo_sz_xGlyphElt ||
 	    (this_glyphset_info != glyphset_info)) {
 	    status = _emit_glyphs_chunk (display, dst, glyphs, i,
 					 scaled_font, op, src, attributes,