diff --git a/exa/exa_glyphs.c b/exa/exa_glyphs.c
index 5c46ec9..1a41c5a 100644
--- a/exa/exa_glyphs.c
+++ b/exa/exa_glyphs.c
@@ -704,6 +704,7 @@ exaGlyphs (CARD8 	 op,
     PixmapPtr   pMaskPixmap = 0;
     PicturePtr  pMask = NULL;
     ScreenPtr   pScreen = pDst->pDrawable->pScreen;
+    ExaScreenPriv(pScreen);
     int		width = 0, height = 0;
     int		x, y;
     int		first_xOff = list->xOff, first_yOff = list->yOff;
@@ -716,7 +717,6 @@ exaGlyphs (CARD8 	 op,
 
     if (maskFormat)
     {
-	ExaScreenPriv(pScreen);
 	GCPtr	    pGC;
 	xRectangle  rect;
 
@@ -738,22 +738,20 @@ exaGlyphs (CARD8 	 op,
 						maskFormat->depth,
 						CREATE_PIXMAP_USAGE_SCRATCH);
 	if (!pMaskPixmap)
-	    return;
+	    goto fallback;
 	component_alpha = NeedsComponent(maskFormat->format);
 	pMask = CreatePicture (0, &pMaskPixmap->drawable,
 			       maskFormat, CPComponentAlpha, &component_alpha,
 			       serverClient, &error);
-	if (!pMask ||
-	    (!component_alpha && pExaScr->info->CheckComposite &&
-	     !(*pExaScr->info->CheckComposite) (PictOpAdd, pSrc, NULL, pMask)))
+	(*pScreen->DestroyPixmap) (pMaskPixmap);
+	if (!pMask)
+	    goto fallback;
+
+	if (!component_alpha && pExaScr->info->CheckComposite &&
+	    !(*pExaScr->info->CheckComposite) (PictOpAdd, pSrc, NULL, pMask))
 	{
 	    PictFormatPtr argbFormat;
 
-	    (*pScreen->DestroyPixmap) (pMaskPixmap);
-
-	    if (!pMask)
-		return;
-
 	    /* The driver can't seem to composite to a8, let's try argb (but
 	     * without component-alpha) */
 	    FreePicture ((pointer) pMask, (XID) 0);
@@ -767,15 +765,25 @@ exaGlyphs (CARD8 	 op,
 						    maskFormat->depth,
 						    CREATE_PIXMAP_USAGE_SCRATCH);
 	    if (!pMaskPixmap)
-		return;
+		goto fallback;
 
 	    pMask = CreatePicture (0, &pMaskPixmap->drawable, maskFormat, 0, 0,
 				   serverClient, &error);
-	    if (!pMask) {
-		(*pScreen->DestroyPixmap) (pMaskPixmap);
-		return;
-	    }
+	    (*pScreen->DestroyPixmap) (pMaskPixmap);
+	    if (!pMask)
+		goto fallback;
 	}
+
+	if (pExaScr->info->CheckComposite &&
+	    (!(*pExaScr->info->CheckComposite) (PictOpAdd, pSrc, NULL, pMask) ||
+	     (!(*pExaScr->info->CheckComposite) (op, pSrc, pMask, pDst) &&
+	      (op != PictOpOver ||
+	       !(*pExaScr->info->CheckComposite) (PictOpOutReverse, pSrc, pMask, pDst) ||
+	       !(*pExaScr->info->CheckComposite) (PictOpOver, pSrc, pMask, pDst))))) {
+	    FreePicture ((pointer) pMask, (XID) 0);
+	    goto fallback;
+	}
+
 	pGC = GetScratchGC (pMaskPixmap->drawable.depth, pScreen);
 	ValidateGC (&pMaskPixmap->drawable, pGC);
 	rect.x = 0;
@@ -789,6 +797,13 @@ exaGlyphs (CARD8 	 op,
     }
     else
     {
+	if (pExaScr->info->CheckComposite &&
+	    !(*pExaScr->info->CheckComposite) (op, pSrc, NULL, pDst) &&
+	    (op != PictOpOver ||
+	     !(*pExaScr->info->CheckComposite) (PictOpOutReverse, pSrc, NULL, pDst) ||
+	     !(*pExaScr->info->CheckComposite) (PictOpOver, pSrc, NULL, pDst)))
+	    goto fallback;
+
 	x = 0;
 	y = 0;
     }
@@ -858,6 +873,10 @@ exaGlyphs (CARD8 	 op,
 			  x, y,
 			  width, height);
 	FreePicture ((pointer) pMask, (XID) 0);
-	(*pScreen->DestroyPixmap) (pMaskPixmap);
     }
+
+    return;
+
+fallback:
+    ExaCheckGlyphs(op, pSrc, pDst, maskFormat, xSrc, ySrc, nlist, list, glyphs);
 }
diff --git a/exa/exa_render.c b/exa/exa_render.c
index 3974afe..d1c363a 100644
--- a/exa/exa_render.c
+++ b/exa/exa_render.c
@@ -902,7 +902,7 @@ exaComposite(CARD8	op,
     Bool saveMaskRepeat = pMask ? pMask->repeat : 0;
     RegionRec region;
 
-    if (pExaScr->swappedOut)
+    if (pExaScr->fallback_counter || pExaScr->swappedOut)
 	goto fallback;
 
     /* Remove repeat in source if useless */
diff --git a/exa/exa_unaccel.c b/exa/exa_unaccel.c
index 219f903..0dd59d7 100644
--- a/exa/exa_unaccel.c
+++ b/exa/exa_unaccel.c
@@ -697,6 +697,7 @@ ExaCheckGlyphs (CARD8	      op,
     ScreenPtr pScreen = pDst->pDrawable->pScreen;
     EXA_PRE_FALLBACK(pScreen);
 
+    exaPrepareAccess (pDst->pDrawable, EXA_PREPARE_DEST);
     miGlyphs(op, pSrc, pDst, maskFormat, xSrc, ySrc, nlist, list, glyphs);
 
     EXA_POST_FALLBACK(pScreen);