diff --git a/exa/exa.c b/exa/exa.c
index e264d440c..46e91820b 100644
--- a/exa/exa.c
+++ b/exa/exa.c
@@ -774,10 +774,18 @@ ExaBlockHandler(int screenNum, pointer blockData, pointer pTimeout,
     ScreenPtr pScreen = screenInfo.screens[screenNum];
     ExaScreenPriv(pScreen);
 
+    /* Move any deferred results from a software fallback to the driver pixmap */
+    if (pExaScr->deferred_mixed_pixmap)
+	exaMoveInPixmap_mixed(pExaScr->deferred_mixed_pixmap);
+
     unwrap(pExaScr, pScreen, BlockHandler);
     (*pScreen->BlockHandler) (screenNum, blockData, pTimeout, pReadmask);
     wrap(pExaScr, pScreen, BlockHandler, ExaBlockHandler);
 
+    /* The rest only applies to classic EXA */
+    if (pExaScr->info->flags & EXA_HANDLES_PIXMAPS)
+	return;
+
     /* Try and keep the offscreen memory area tidy every now and then (at most 
      * once per second) when the server has been idle for at least 100ms.
      */
@@ -991,10 +999,12 @@ exaDriverInit (ScreenPtr		pScreen,
      * Replace various fb screen functions
      */
     if ((pExaScr->info->flags & EXA_OFFSCREEN_PIXMAPS) &&
-	!(pExaScr->info->flags & EXA_HANDLES_PIXMAPS)) {
+	(!(pExaScr->info->flags & EXA_HANDLES_PIXMAPS) ||
+	 (pExaScr->info->flags & EXA_MIXED_PIXMAPS)))
 	wrap(pExaScr, pScreen, BlockHandler, ExaBlockHandler);
+    if ((pExaScr->info->flags & EXA_OFFSCREEN_PIXMAPS) &&
+	!(pExaScr->info->flags & EXA_HANDLES_PIXMAPS))
 	wrap(pExaScr, pScreen, WakeupHandler, ExaWakeupHandler);
-    }
     wrap(pExaScr, pScreen, CreateGC, exaCreateGC);
     wrap(pExaScr, pScreen, CloseScreen, exaCloseScreen);
     wrap(pExaScr, pScreen, GetImage, exaGetImage);
diff --git a/exa/exa_migration_mixed.c b/exa/exa_migration_mixed.c
index f42c9c233..6065d7577 100644
--- a/exa/exa_migration_mixed.c
+++ b/exa/exa_migration_mixed.c
@@ -99,8 +99,13 @@ exaDoMigration_mixed(ExaMigrationPtr pixmaps, int npixmaps, Bool can_accel)
 	    exaCreateDriverPixmap_mixed(pPixmap);
 
 	if (pExaPixmap->pDamage && exaPixmapIsOffscreen(pPixmap)) {
+	    ExaScreenPriv(pPixmap->drawable.pScreen);
+
 	    pPixmap->devKind = pExaPixmap->fb_pitch;
 	    exaCopyDirtyToFb(pixmaps + i);
+
+	    if (pExaScr->deferred_mixed_pixmap == pPixmap)
+		pExaScr->deferred_mixed_pixmap = NULL;
 	}
 
 	pExaPixmap->offscreen = exaPixmapIsOffscreen(pPixmap);
@@ -197,6 +202,9 @@ exaPrepareAccessReg_mixed(PixmapPtr pPixmap, int index, RegionPtr pReg)
 
 /* Move back results of software rendering on system memory copy of mixed driver
  * pixmap (see exaPrepareAccessReg_mixed).
+ *
+ * Defer moving the destination back into the driver pixmap, to try and save
+ * overhead on multiple consequent software fallbacks.
  */
 void exaFinishAccess_mixed(PixmapPtr pPixmap, int index)
 {
@@ -204,6 +212,16 @@ void exaFinishAccess_mixed(PixmapPtr pPixmap, int index)
 
     if (pExaPixmap->pDamage && exaPixmapIsOffscreen(pPixmap)) {
 	DamageRegionProcessPending(&pPixmap->drawable);
-	exaMoveInPixmap_mixed(pPixmap);
+
+	if (index == EXA_PREPARE_DEST || index == EXA_PREPARE_AUX_DEST) {
+	    ExaScreenPriv(pPixmap->drawable.pScreen);
+
+	    if (pExaScr->deferred_mixed_pixmap &&
+		pExaScr->deferred_mixed_pixmap != pPixmap)
+		exaMoveInPixmap_mixed(pExaScr->deferred_mixed_pixmap);
+	    pExaScr->deferred_mixed_pixmap = pPixmap;
+	    pPixmap->devKind = pExaPixmap->fb_pitch;
+	} else
+	    exaMoveInPixmap_mixed(pPixmap);
     }
 }
diff --git a/exa/exa_mixed.c b/exa/exa_mixed.c
index 167ffa9d5..bc393c772 100644
--- a/exa/exa_mixed.c
+++ b/exa/exa_mixed.c
@@ -192,6 +192,9 @@ exaDestroyPixmap_mixed(PixmapPtr pPixmap)
     {
 	ExaPixmapPriv (pPixmap);
 
+	if (pExaScr->deferred_mixed_pixmap == pPixmap)
+	    pExaScr->deferred_mixed_pixmap = NULL;
+
 	if (pExaPixmap->driverPriv)
 	    pExaScr->info->DestroyPixmap(pScreen, pExaPixmap->driverPriv);
 	pExaPixmap->driverPriv = NULL;
diff --git a/exa/exa_priv.h b/exa/exa_priv.h
index 1aec8e966..5b056dab9 100644
--- a/exa/exa_priv.h
+++ b/exa/exa_priv.h
@@ -188,6 +188,7 @@ typedef struct {
     unsigned			 numOffscreenAvailable;
     CARD32			 lastDefragment;
     CARD32			 nextDefragment;
+    PixmapPtr			 deferred_mixed_pixmap;
 
     /* Reference counting for accessed pixmaps */
     struct {