diff --git a/mlir/lib/Dialect/Async/Transforms/AsyncParallelFor.cpp b/mlir/lib/Dialect/Async/Transforms/AsyncParallelFor.cpp
--- a/mlir/lib/Dialect/Async/Transforms/AsyncParallelFor.cpp
+++ b/mlir/lib/Dialect/Async/Transforms/AsyncParallelFor.cpp
@@ -252,12 +252,9 @@
   Value blockFirstIndex = b.create<arith::MulIOp>(blockIndex, blockSize);
 
   // The last one-dimensional index in the block defined by the `blockIndex`:
-  //   blockLastIndex = max(blockFirstIndex + blockSize, tripCount) - 1
   Value blockEnd0 = b.create<arith::AddIOp>(blockFirstIndex, blockSize);
-  Value blockEnd1 =
-      b.create<arith::CmpIOp>(arith::CmpIPredicate::sge, blockEnd0, tripCount);
-  Value blockEnd2 = b.create<SelectOp>(blockEnd1, tripCount, blockEnd0);
-  Value blockLastIndex = b.create<arith::SubIOp>(blockEnd2, c1);
+  Value blockEnd1 = b.create<arith::MinSIOp>(blockEnd0, tripCount);
+  Value blockLastIndex = b.create<arith::SubIOp>(blockEnd1, c1);
 
   // Convert one-dimensional indices to multi-dimensional coordinates.
   auto blockFirstCoord = delinearize(b, blockFirstIndex, tripCounts);
@@ -696,17 +693,9 @@
     //   blockSize = min(tripCount,
     //                   max(ceil_div(tripCount, maxComputeBlocks),
     //                       ceil_div(minTaskSize, bodySize)))
-    Value bs0 = b.create<arith::DivSIOp>(tripCount, maxComputeBlocks);
-    Value bs1 =
-        b.create<arith::CmpIOp>(arith::CmpIPredicate::sge, bs0, minTaskSizeCst);
-    Value bs2 = b.create<SelectOp>(bs1, bs0, minTaskSizeCst);
-    Value bs3 =
-        b.create<arith::CmpIOp>(arith::CmpIPredicate::sle, tripCount, bs2);
-    Value blockSize0 = b.create<SelectOp>(bs3, tripCount, bs2);
-    Value blockCount0 = b.create<arith::CeilDivSIOp>(tripCount, blockSize0);
-
-    // Compute balanced block size for the estimated block count.
-    Value blockSize = b.create<arith::CeilDivSIOp>(tripCount, blockCount0);
+    Value bs0 = b.create<arith::CeilDivSIOp>(tripCount, maxComputeBlocks);
+    Value bs1 = b.create<arith::MaxSIOp>(bs0, minTaskSizeCst);
+    Value blockSize = b.create<arith::MinSIOp>(tripCount, bs1);
     Value blockCount = b.create<arith::CeilDivSIOp>(tripCount, blockSize);
 
     // Create a parallel compute function that takes a block id and computes the
diff --git a/mlir/test/Integration/Dialect/Async/CPU/test-async-parallel-for-2d.mlir b/mlir/test/Integration/Dialect/Async/CPU/test-async-parallel-for-2d.mlir
--- a/mlir/test/Integration/Dialect/Async/CPU/test-async-parallel-for-2d.mlir
+++ b/mlir/test/Integration/Dialect/Async/CPU/test-async-parallel-for-2d.mlir
@@ -2,6 +2,7 @@
 // RUN:               -async-to-async-runtime                                  \
 // RUN:               -async-runtime-ref-counting                              \
 // RUN:               -async-runtime-ref-counting-opt                          \
+// RUN:               -arith-expand                                            \
 // RUN:               -convert-async-to-llvm                                   \
 // RUN:               -convert-scf-to-std                                      \
 // RUN:               -convert-memref-to-llvm                                  \
@@ -16,6 +17,7 @@
 // RUN:   mlir-opt %s -async-parallel-for                                      \
 // RUN:               -async-to-async-runtime                                  \
 // RUN:               -async-runtime-policy-based-ref-counting                 \
+// RUN:               -arith-expand                                            \
 // RUN:               -convert-async-to-llvm                                   \
 // RUN:               -convert-scf-to-std                                      \
 // RUN:               -convert-memref-to-llvm                                  \
@@ -33,6 +35,7 @@
 // RUN:               -async-to-async-runtime                                  \
 // RUN:               -async-runtime-ref-counting                              \
 // RUN:               -async-runtime-ref-counting-opt                          \
+// RUN:               -arith-expand                                            \
 // RUN:               -convert-async-to-llvm                                   \
 // RUN:               -convert-scf-to-std                                      \
 // RUN:               -convert-memref-to-llvm                                  \