diff --git a/pkg/distsql/request_builder.go b/pkg/distsql/request_builder.go
index da6a6eda7b8d4..29d192c913a3b 100644
--- a/pkg/distsql/request_builder.go
+++ b/pkg/distsql/request_builder.go
@@ -44,6 +44,9 @@ type RequestBuilder struct {
 	kv.Request
 	is  infoschema.InfoSchema
 	err error
+
+	// When SetDAGRequest is called, builder will also this field.
+	dag *tipb.DAGRequest
 }
 
 // Build builds a "kv.Request".
@@ -72,6 +75,29 @@ func (builder *RequestBuilder) Build() (*kv.Request, error) {
 	if builder.Request.KeyRanges == nil {
 		builder.Request.KeyRanges = kv.NewNonParitionedKeyRanges(nil)
 	}
+
+	if dag := builder.dag; dag != nil {
+		if execCnt := len(dag.Executors); execCnt == 1 {
+			oldConcurrency := builder.Request.Concurrency
+			// select * from t order by id
+			if builder.Request.KeepOrder {
+				// When the DAG is just simple scan and keep order, set concurrency to 2.
+				// If a lot data are returned to client, mysql protocol is the bottleneck so concurrency 2 is enough.
+				// If very few data are returned to client, the speed is not optimal but good enough.
+				switch dag.Executors[0].Tp {
+				case tipb.ExecType_TypeTableScan, tipb.ExecType_TypeIndexScan, tipb.ExecType_TypePartitionTableScan:
+					builder.Request.Concurrency = 2
+					failpoint.Inject("testRateLimitActionMockConsumeAndAssert", func(val failpoint.Value) {
+						if val.(bool) {
+							// When the concurrency is too small, test case tests/realtikvtest/sessiontest.TestCoprocessorOOMAction can't trigger OOM condition
+							builder.Request.Concurrency = oldConcurrency
+						}
+					})
+				}
+			}
+		}
+	}
+
 	return &builder.Request, builder.err
 }
 
@@ -151,17 +177,18 @@ func (builder *RequestBuilder) SetDAGRequest(dag *tipb.DAGRequest) *RequestBuild
 		builder.Request.Tp = kv.ReqTypeDAG
 		builder.Request.Cacheable = true
 		builder.Request.Data, builder.err = dag.Marshal()
-	}
-	if execCnt := len(dag.Executors); execCnt != 0 && dag.Executors[execCnt-1].GetLimit() != nil {
-		limit := dag.Executors[execCnt-1].GetLimit()
-		builder.Request.LimitSize = limit.GetLimit()
-		// When the DAG is just simple scan and small limit, set concurrency to 1 would be sufficient.
-		if execCnt == 2 {
-			if limit.Limit < estimatedRegionRowCount {
-				if kr := builder.Request.KeyRanges; kr != nil {
-					builder.Request.Concurrency = kr.PartitionNum()
-				} else {
-					builder.Request.Concurrency = 1
+		builder.dag = dag
+		if execCnt := len(dag.Executors); execCnt != 0 && dag.Executors[execCnt-1].GetLimit() != nil {
+			limit := dag.Executors[execCnt-1].GetLimit()
+			builder.Request.LimitSize = limit.GetLimit()
+			// When the DAG is just simple scan and small limit, set concurrency to 1 would be sufficient.
+			if execCnt == 2 {
+				if limit.Limit < estimatedRegionRowCount {
+					if kr := builder.Request.KeyRanges; kr != nil {
+						builder.Request.Concurrency = kr.PartitionNum()
+					} else {
+						builder.Request.Concurrency = 1
+					}
 				}
 			}
 		}
diff --git a/pkg/session/test/variable/variable_test.go b/pkg/session/test/variable/variable_test.go
index a882f536108a5..791c989ef537d 100644
--- a/pkg/session/test/variable/variable_test.go
+++ b/pkg/session/test/variable/variable_test.go
@@ -93,6 +93,11 @@ func TestCoprocessorOOMAction(t *testing.T) {
 			sql:  "select id from t5",
 		},
 	}
+
+	require.NoError(t, failpoint.Enable("github.com/pingcap/tidb/pkg/distsql/testRateLimitActionMockConsumeAndAssert", `return(true)`))
+	defer func() {
+		require.NoError(t, failpoint.Disable("github.com/pingcap/tidb/pkg/distsql/testRateLimitActionMockConsumeAndAssert"))
+	}()
 	require.NoError(t, failpoint.Enable("github.com/pingcap/tidb/pkg/store/copr/testRateLimitActionMockConsumeAndAssert", `return(true)`))
 	defer func() {
 		require.NoError(t, failpoint.Disable("github.com/pingcap/tidb/pkg/store/copr/testRateLimitActionMockConsumeAndAssert"))
diff --git a/pkg/store/copr/coprocessor.go b/pkg/store/copr/coprocessor.go
index 93b80a138a6fe..810b6910b2512 100644
--- a/pkg/store/copr/coprocessor.go
+++ b/pkg/store/copr/coprocessor.go
@@ -207,31 +207,6 @@ func (c *CopClient) BuildCopIterator(ctx context.Context, req *kv.Request, vars
 	}
 
 	if it.req.KeepOrder {
-		// Don't set high concurrency for the keep order case. It wastes a lot of memory and gains nothing.
-		// TL;DR
-		// Because for a keep order coprocessor request, the cop tasks are handled one by one, if we set a
-		// higher concurrency, the data is just cached and not consumed for a while, this increase the memory usage.
-		// Set concurrency to 2 can reduce the memory usage and I've tested that it does not necessarily
-		// decrease the performance.
-		// For ReqTypeAnalyze, we keep its concurrency to avoid slow analyze(see https://github.com/pingcap/tidb/issues/40162 for details).
-		if it.concurrency > 2 && it.req.Tp != kv.ReqTypeAnalyze {
-			oldConcurrency := it.concurrency
-			partitionNum := req.KeyRanges.PartitionNum()
-			if partitionNum > it.concurrency {
-				partitionNum = it.concurrency
-			}
-			it.concurrency = 2
-			if it.concurrency < partitionNum {
-				it.concurrency = partitionNum
-			}
-
-			failpoint.Inject("testRateLimitActionMockConsumeAndAssert", func(val failpoint.Value) {
-				if val.(bool) {
-					// When the concurrency is too small, test case tests/realtikvtest/sessiontest.TestCoprocessorOOMAction can't trigger OOM condition
-					it.concurrency = oldConcurrency
-				}
-			})
-		}
 		if it.smallTaskConcurrency > 20 {
 			it.smallTaskConcurrency = 20
 		}