diff --git a/src/sna/gen6_render.c b/src/sna/gen6_render.c
index afebab40..7878e7bc 100644
--- a/src/sna/gen6_render.c
+++ b/src/sna/gen6_render.c
@@ -2684,6 +2684,9 @@ static inline bool prefer_blt_copy(struct sna *sna,
 	if (sna->kgem.ring == KGEM_BLT)
 		return true;
 
+	if (flags & COPY_DRI && !sna->kgem.has_semaphores)
+		return false;
+
 	if ((flags & COPY_SMALL || src_bo == dst_bo) &&
 	    can_switch_to_blt(sna, dst_bo, flags))
 		return true;
diff --git a/src/sna/gen7_render.c b/src/sna/gen7_render.c
index 87807860..39f0d385 100644
--- a/src/sna/gen7_render.c
+++ b/src/sna/gen7_render.c
@@ -2890,6 +2890,9 @@ prefer_blt_copy(struct sna *sna,
 	    untiled_tlb_miss(dst_bo))
 		return true;
 
+	if (flags & COPY_DRI && !sna->kgem.has_semaphores)
+		return false;
+
 	if (force_blt_ring(sna))
 		return true;
 
@@ -2903,6 +2906,7 @@ prefer_blt_copy(struct sna *sna,
 		return false;
 
 	if (flags & COPY_LAST &&
+	    sna->render_state.gt < 3 &&
             can_switch_to_blt(sna, dst_bo, flags))
 		return true;
 
diff --git a/src/sna/gen8_render.c b/src/sna/gen8_render.c
index 043e268d..ebabb2e5 100644
--- a/src/sna/gen8_render.c
+++ b/src/sna/gen8_render.c
@@ -2713,6 +2713,9 @@ prefer_blt_copy(struct sna *sna,
 	    untiled_tlb_miss(dst_bo))
 		return true;
 
+	if (flags & COPY_DRI && !sna->kgem.has_semaphores)
+		return false;
+
 	if (force_blt_ring(sna))
 		return true;
 
@@ -2726,6 +2729,7 @@ prefer_blt_copy(struct sna *sna,
 		return false;
 
 	if (flags & COPY_LAST &&
+	    sna->render_state.gt < 3 &&
             can_switch_to_blt(sna, dst_bo, flags))
 		return true;
 
diff --git a/src/sna/sna_dri2.c b/src/sna/sna_dri2.c
index 83e652da..7868d037 100644
--- a/src/sna/sna_dri2.c
+++ b/src/sna/sna_dri2.c
@@ -246,7 +246,7 @@ sna_dri2_get_back(struct sna *sna,
 			if (sna->render.copy_boxes(sna, GXcopy,
 						   draw, get_private(back)->bo, 0, 0,
 						   draw, bo, 0, 0,
-						   &box, 1, 0))
+						   &box, 1, COPY_LAST | COPY_DRI))
 				flags = back->flags;
 		}
 	}
@@ -1155,7 +1155,7 @@ __sna_dri2_copy_region(struct sna *sna, DrawablePtr draw, RegionPtr region,
 	     boxes[0].x2, boxes[0].y2,
 	     n, sx, sy, dx, dy));
 
-	hint = COPY_LAST;
+	hint = COPY_LAST | COPY_DRI;
 	if (flags & DRI2_SYNC)
 		hint |= COPY_SYNC;
 	if (!sna->render.copy_boxes(sna, GXcopy,
diff --git a/src/sna/sna_render.h b/src/sna/sna_render.h
index dcc0ddd4..f59a9283 100644
--- a/src/sna/sna_render.h
+++ b/src/sna/sna_render.h
@@ -287,6 +287,7 @@ struct sna_render {
 #define COPY_SYNC 0x2
 #define COPY_NO_OVERLAP 0x4
 #define COPY_SMALL 0x8
+#define COPY_DRI 0x10
 
 	bool (*copy)(struct sna *sna, uint8_t alu,
 		     PixmapPtr src, struct kgem_bo *src_bo,