diff --git a/Makefile b/Makefile
index 9200683f459f8..a10eaef06b208 100644
--- a/Makefile
+++ b/Makefile
@@ -436,8 +436,8 @@ bazel_test: failpoint-enable bazel_ci_prepare
 
 bazel_coverage_test: failpoint-enable bazel_ci_prepare
 	bazel --output_user_root=/home/jenkins/.tidb/tmp coverage --config=ci --@io_bazel_rules_go//go/config:cover_format=go_cover \
-		-- //... -//cmd/... -//tests/... \
-		-//br/pkg/task:task_test
+		-- //... -//cmd/... -//tests/graceshutdown/... \
+		-//tests/globalkilltest/... -//tests/readonlytest/... -//br/pkg/task:task_test
 
 bazel_build: bazel_ci_prepare
 	mkdir -p bin
diff --git a/store/copr/coprocessor.go b/store/copr/coprocessor.go
index 161da48b39a1c..eb151254d2a26 100644
--- a/store/copr/coprocessor.go
+++ b/store/copr/coprocessor.go
@@ -127,7 +127,15 @@ func (c *CopClient) Send(ctx context.Context, req *kv.Request, variables interfa
 		// Set concurrency to 2 can reduce the memory usage and I've tested that it does not necessarily
 		// decrease the performance.
 		if it.concurrency > 2 {
+			oldConcurrency := it.concurrency
 			it.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
+					it.concurrency = oldConcurrency
+				}
+			})
 		}
 		it.sendRate = util.NewRateLimit(2 * it.concurrency)
 		it.respChan = nil