diff --git a/hadoop-mapreduce-project/hadoop-mapreduce-client/hadoop-mapreduce-client-app/src/main/java/org/apache/hadoop/mapreduce/v2/app/rm/RMContainerAllocator.java b/hadoop-mapreduce-project/hadoop-mapreduce-client/hadoop-mapreduce-client-app/src/main/java/org/apache/hadoop/mapreduce/v2/app/rm/RMContainerAllocator.java
index 1f88a2c70e..09527977de 100644
--- a/hadoop-mapreduce-project/hadoop-mapreduce-client/hadoop-mapreduce-client-app/src/main/java/org/apache/hadoop/mapreduce/v2/app/rm/RMContainerAllocator.java
+++ b/hadoop-mapreduce-project/hadoop-mapreduce-client/hadoop-mapreduce-client-app/src/main/java/org/apache/hadoop/mapreduce/v2/app/rm/RMContainerAllocator.java
@@ -919,7 +919,8 @@ void processFinishedContainer(ContainerStatus container) {
 
   private void applyConcurrentTaskLimits() {
     int numScheduledMaps = scheduledRequests.maps.size();
-    if (maxRunningMaps > 0 && numScheduledMaps > 0) {
+    if (maxRunningMaps > 0 && numScheduledMaps > 0 &&
+        getJob().getTotalMaps() > maxRunningMaps) {
       int maxRequestedMaps = Math.max(0,
           maxRunningMaps - assignedRequests.maps.size());
       int numScheduledFailMaps = scheduledRequests.earlierFailedMaps.size();
@@ -936,7 +937,8 @@ private void applyConcurrentTaskLimits() {
     }
 
     int numScheduledReduces = scheduledRequests.reduces.size();
-    if (maxRunningReduces > 0 && numScheduledReduces > 0) {
+    if (maxRunningReduces > 0 && numScheduledReduces > 0 &&
+        getJob().getTotalReduces() > maxRunningReduces) {
       int maxRequestedReduces = Math.max(0,
           maxRunningReduces - assignedRequests.reduces.size());
       int reduceRequestLimit = Math.min(maxRequestedReduces,
diff --git a/hadoop-mapreduce-project/hadoop-mapreduce-client/hadoop-mapreduce-client-app/src/test/java/org/apache/hadoop/mapreduce/v2/app/rm/TestRMContainerAllocator.java b/hadoop-mapreduce-project/hadoop-mapreduce-client/hadoop-mapreduce-client-app/src/test/java/org/apache/hadoop/mapreduce/v2/app/rm/TestRMContainerAllocator.java
index 933bd013ef..8879362e1b 100644
--- a/hadoop-mapreduce-project/hadoop-mapreduce-client/hadoop-mapreduce-client-app/src/test/java/org/apache/hadoop/mapreduce/v2/app/rm/TestRMContainerAllocator.java
+++ b/hadoop-mapreduce-project/hadoop-mapreduce-client/hadoop-mapreduce-client-app/src/test/java/org/apache/hadoop/mapreduce/v2/app/rm/TestRMContainerAllocator.java
@@ -2781,15 +2781,78 @@ public Token<AMRMTokenIdentifier> run() throws Exception {
         new Text(rmAddr), ugiToken.getService());
   }
 
+  @Test
+  public void testConcurrentTaskLimitsDisabledIfSmaller() throws Exception {
+    final int MAP_COUNT = 1;
+    final int REDUCE_COUNT = 1;
+    final int MAP_LIMIT = 1;
+    final int REDUCE_LIMIT = 1;
+    Configuration conf = new Configuration();
+    conf.setInt(MRJobConfig.JOB_RUNNING_MAP_LIMIT, MAP_LIMIT);
+    conf.setInt(MRJobConfig.JOB_RUNNING_REDUCE_LIMIT, REDUCE_LIMIT);
+    conf.setFloat(MRJobConfig.COMPLETED_MAPS_FOR_REDUCE_SLOWSTART, 0.0f);
+    ApplicationId appId = ApplicationId.newInstance(1, 1);
+    ApplicationAttemptId appAttemptId =
+        ApplicationAttemptId.newInstance(appId, 1);
+    JobId jobId = MRBuilderUtils.newJobId(appAttemptId.getApplicationId(), 0);
+    Job mockJob = mock(Job.class);
+    when(mockJob.getReport()).thenReturn(
+        MRBuilderUtils.newJobReport(jobId, "job", "user", JobState.RUNNING, 0,
+            0, 0, 0, 0, 0, 0, "jobfile", null, false, ""));
+    when(mockJob.getTotalMaps()).thenReturn(MAP_COUNT);
+    when(mockJob.getTotalReduces()).thenReturn(REDUCE_COUNT);
+
+    final MockScheduler mockScheduler = new MockScheduler(appAttemptId);
+    MyContainerAllocator allocator =
+        new MyContainerAllocator(null, conf, appAttemptId, mockJob,
+            SystemClock.getInstance()) {
+          @Override
+          protected void register() {
+          }
+
+          @Override
+          protected ApplicationMasterProtocol createSchedulerProxy() {
+            return mockScheduler;
+          }
+
+          @Override
+          protected void setRequestLimit(Priority priority,
+              Resource capability, int limit) {
+            Assert.fail("setRequestLimit() should not be invoked");
+          }
+        };
+
+    // create some map requests
+    ContainerRequestEvent[] reqMapEvents = new ContainerRequestEvent[MAP_COUNT];
+    for (int i = 0; i < reqMapEvents.length; ++i) {
+      reqMapEvents[i] = createReq(jobId, i, 1024, new String[] { "h" + i });
+    }
+    allocator.sendRequests(Arrays.asList(reqMapEvents));
+    // create some reduce requests
+    ContainerRequestEvent[] reqReduceEvents =
+        new ContainerRequestEvent[REDUCE_COUNT];
+    for (int i = 0; i < reqReduceEvents.length; ++i) {
+      reqReduceEvents[i] =
+          createReq(jobId, i, 1024, new String[] {}, false, true);
+    }
+    allocator.sendRequests(Arrays.asList(reqReduceEvents));
+    allocator.schedule();
+    allocator.schedule();
+    allocator.schedule();
+    allocator.close();
+  }
+
   @Test
   public void testConcurrentTaskLimits() throws Exception {
+    final int MAP_COUNT = 5;
+    final int REDUCE_COUNT = 2;
     final int MAP_LIMIT = 3;
     final int REDUCE_LIMIT = 1;
     LOG.info("Running testConcurrentTaskLimits");
     Configuration conf = new Configuration();
     conf.setInt(MRJobConfig.JOB_RUNNING_MAP_LIMIT, MAP_LIMIT);
     conf.setInt(MRJobConfig.JOB_RUNNING_REDUCE_LIMIT, REDUCE_LIMIT);
-    conf.setFloat(MRJobConfig.COMPLETED_MAPS_FOR_REDUCE_SLOWSTART, 1.0f);
+    conf.setFloat(MRJobConfig.COMPLETED_MAPS_FOR_REDUCE_SLOWSTART, 0.0f);
     ApplicationId appId = ApplicationId.newInstance(1, 1);
     ApplicationAttemptId appAttemptId = ApplicationAttemptId.newInstance(
         appId, 1);
@@ -2798,6 +2861,9 @@ public void testConcurrentTaskLimits() throws Exception {
     when(mockJob.getReport()).thenReturn(
         MRBuilderUtils.newJobReport(jobId, "job", "user", JobState.RUNNING, 0,
             0, 0, 0, 0, 0, 0, "jobfile", null, false, ""));
+    when(mockJob.getTotalMaps()).thenReturn(MAP_COUNT);
+    when(mockJob.getTotalReduces()).thenReturn(REDUCE_COUNT);
+
     final MockScheduler mockScheduler = new MockScheduler(appAttemptId);
     MyContainerAllocator allocator = new MyContainerAllocator(null, conf,
         appAttemptId, mockJob, SystemClock.getInstance()) {
@@ -2812,14 +2878,13 @@ protected ApplicationMasterProtocol createSchedulerProxy() {
     };
 
     // create some map requests
-    ContainerRequestEvent[] reqMapEvents = new ContainerRequestEvent[5];
+    ContainerRequestEvent[] reqMapEvents = new ContainerRequestEvent[MAP_COUNT];
     for (int i = 0; i < reqMapEvents.length; ++i) {
       reqMapEvents[i] = createReq(jobId, i, 1024, new String[] { "h" + i });
     }
     allocator.sendRequests(Arrays.asList(reqMapEvents));
-
     // create some reduce requests
-    ContainerRequestEvent[] reqReduceEvents = new ContainerRequestEvent[2];
+    ContainerRequestEvent[] reqReduceEvents = new ContainerRequestEvent[REDUCE_COUNT];
     for (int i = 0; i < reqReduceEvents.length; ++i) {
       reqReduceEvents[i] = createReq(jobId, i, 1024, new String[] {},
           false, true);