diff --git a/src/sna/sna_composite.c b/src/sna/sna_composite.c
index d19dc42e..f01f020e 100644
--- a/src/sna/sna_composite.c
+++ b/src/sna/sna_composite.c
@@ -696,8 +696,8 @@ sna_composite(CARD8 op,
 		goto fallback;
 	}
 
-	if (dst->alphaMap) {
-		DBG(("%s: fallback due to unhandled alpha-map\n", __FUNCTION__));
+	if (!can_render_to_picture(dst)) {
+		DBG(("%s: fallback due to unhandled picture\n", __FUNCTION__));
 		goto fallback;
 	}
 
@@ -956,8 +956,8 @@ sna_composite_rectangles(CARD8		 op,
 	if (wedged(sna))
 		goto fallback;
 
-	if (dst->alphaMap) {
-		DBG(("%s: fallback, dst has an alpha-map\n", __FUNCTION__));
+	if (!can_render_to_picture(dst)) {
+		DBG(("%s: fallback, dst has an incompatible picture\n", __FUNCTION__));
 		goto fallback;
 	}
 
diff --git a/src/sna/sna_glyphs.c b/src/sna/sna_glyphs.c
index a4052c6e..a5dfb06b 100644
--- a/src/sna/sna_glyphs.c
+++ b/src/sna/sna_glyphs.c
@@ -1971,8 +1971,8 @@ sna_glyphs(CARD8 op,
 		goto fallback;
 	}
 
-	if (dst->alphaMap) {
-		DBG(("%s: fallback -- dst alpha map\n", __FUNCTION__));
+	if (!can_render_to_picture(dst)) {
+		DBG(("%s: fallback -- dst incompatible picture\n", __FUNCTION__));
 		goto fallback;
 	}
 
@@ -2301,8 +2301,8 @@ sna_glyphs__shared(CARD8 op,
 		goto fallback;
 	}
 
-	if (dst->alphaMap) {
-		DBG(("%s: fallback -- dst alpha map\n", __FUNCTION__));
+	if (!can_render_to_picture(dst)) {
+		DBG(("%s: fallback -- incompatible picture\n", __FUNCTION__));
 		goto fallback;
 	}
 
diff --git a/src/sna/sna_render_inline.h b/src/sna/sna_render_inline.h
index 3d24c5c8..10fbbfe2 100644
--- a/src/sna/sna_render_inline.h
+++ b/src/sna/sna_render_inline.h
@@ -112,6 +112,30 @@ too_small(struct sna_pixmap *priv)
 	return (priv->create & KGEM_CAN_CREATE_GPU) == 0;
 }
 
+static inline bool
+can_render_to_picture(PicturePtr dst)
+{
+	if (dst->alphaMap) {
+		DBG(("%s(pixmap=%ld) -- no, has alphamap\n", __FUNCTION__,
+		     get_drawable_pixmap(dst->pDrawable)->drawable.serialNumber));
+		return false;
+	}
+
+	switch (PICT_FORMAT_TYPE(dst->format)) {
+	case PICT_TYPE_COLOR:
+	case PICT_TYPE_GRAY:
+	case PICT_TYPE_OTHER:
+		DBG(("%s(pixmap=%ld) -- no, has palette\n", __FUNCTION__,
+		     get_drawable_pixmap(dst->pDrawable)->drawable.serialNumber));
+		return false;
+	default:
+		break;
+	}
+
+	return true;
+}
+
+
 static inline bool
 is_gpu_dst(struct sna_pixmap *priv)
 {