diff --git a/src/intel/compiler/jay/jay_register_allocate.c b/src/intel/compiler/jay/jay_register_allocate.c
index e1ee4211185..ae998521829 100644
--- a/src/intel/compiler/jay/jay_register_allocate.c
+++ b/src/intel/compiler/jay/jay_register_allocate.c
@@ -595,18 +595,28 @@ jay_emit_parallel_copies(jay_builder *b,
          jay_def dst = def_from_reg(copy->dst), src = def_from_reg(copy->src);
          assert(dst.file == src.file);
          enum jay_file file = dst.file;
-         struct jay_temp_regs t = { .gpr = temps.gpr2, .ugpr = temps.ugpr2 };
-         jay_def temp_backing = jay_null();
-         jay_def temp =
-            push_temp(b, temps, file == GPR || file == MEM ? GPR : UGPR,
-                      file == MEM /* stride4 */, true /* outer */,
-                      &temp_backing, dst, src);
-         {
+
+         if (file == GPR &&
+             jay_def_stride(b->shader, dst) == JAY_STRIDE_4 &&
+             jay_def_stride(b->shader, src) == JAY_STRIDE_4) {
+
+            /* If everything is stride=4, swapping is easy */
+            jay_def acc = jay_bare_reg(ACCUM, 2);
+            jay_MOV(b, acc, dst)->type = JAY_TYPE_F32;
+            jay_MOV(b, dst, src)->type = JAY_TYPE_F32;
+            jay_MOV(b, src, acc)->type = JAY_TYPE_F32;
+         } else {
+            struct jay_temp_regs t = { .gpr = temps.gpr2, .ugpr = temps.ugpr2 };
+            jay_def temp_backing = jay_null();
+            jay_def temp =
+               push_temp(b, temps, file == GPR || file == MEM ? GPR : UGPR,
+                         file == MEM /* stride4 */, true /* outer */,
+                         &temp_backing, dst, src);
             mov(b, temp, dst, t);
             mov(b, dst, src, t);
             mov(b, src, temp, t);
+            pop_temp(b, temp, temp_backing);
          }
-         pop_temp(b, temp, temp_backing);
 
          for (unsigned j = 0; j < num_copies; j++) {
             if (pcopies[j].src == copy->dst)