diff --git a/third_party/intel/lib/TritonIntelGPUToLLVM/ConvertLayoutOpToLLVM.cpp b/third_party/intel/lib/TritonIntelGPUToLLVM/ConvertLayoutOpToLLVM.cpp
index 6b7f1e78e7..d5e003d90e 100644
--- a/third_party/intel/lib/TritonIntelGPUToLLVM/ConvertLayoutOpToLLVM.cpp
+++ b/third_party/intel/lib/TritonIntelGPUToLLVM/ConvertLayoutOpToLLVM.cpp
@@ -488,17 +488,20 @@ struct ConvertLayoutOpUsingLinearLayoutsConversion
     assert(to_vector(conversion->getInDimNames()) ==
            to_vector(conversion->getOutDimNames()));
     auto dims = conversion->getInDimNames();
-    if (llvm::is_contained(dims, str_attr("block"))) {
+    if (llvm::is_contained(dims, kBlock)) {
       // Case 1: Transfer between values in different CTAs.
       //          This requires moving values through distributed shared memory.
       return rewriter.notifyMatchFailure(
           op, "NYI: Transfer between different CTAs");
-    } else if (llvm::is_contained(dims, str_attr("warp"))) {
-      return rewriter.notifyMatchFailure(
-          op, "NYI: Transfer between different warps");
-    } else if (llvm::is_contained(dims, str_attr("lane"))) {
+    } else if (llvm::is_contained(dims, kWarp)) {
       // Case 2: Transfer between values in the same CTA, in which case we move
       //         values through shared memory.
+      // TODO: Implement
+      return failure();
+    } else if (llvm::is_contained(dims, kLane)) {
+      // Case 3. Transfer between values in the same warp, in which case we try
+      //         to move values using warp shuffles, though if the pattern is
+      //         complicated enough we may fall back to using shared memory
       // If the operation is a supported sub-group shuffle, perform via shuffle
       // operations.
       if (intel::cvtIsSubGroupShuffle(srcTy, dstTy)) {
@@ -513,15 +516,17 @@ struct ConvertLayoutOpUsingLinearLayoutsConversion
       }
       // TODO(jlebar): Implement me.
       return failure();
-    } else if (llvm::is_contained(dims, str_attr("register"))) {
+    } else if (llvm::is_contained(dims, kRegister) ||
+               dstLayout.getInDimSize(kRegister) !=
+                   srcLayout.getInDimSize(kRegister)) {
       // Case 4. Transfer between values in the same thread, in which case we
       //         simply reorder the elements of adaptor.getSrc().
       return transferWithinThread(
           op, dstLayout.getFreeVariableMasks()[kRegister],
           dstLayout.getInDimSize(kRegister), *conversion, adaptor, rewriter);
     } else {
-      // The two layouts are equivalent. We should probably remove these in
-      // RemoveLayoutConversion.
+      // Cast 5. The two layouts are equivalent. We should probably remove
+      // these in RemoveLayoutConversion.
       rewriter.replaceOp(op, adaptor.getSrc());
       return success();
     }