diff --git a/test/e2e/apps/job.go b/test/e2e/apps/job.go
index 0f08c885ec0..9fd7111f5b7 100644
--- a/test/e2e/apps/job.go
+++ b/test/e2e/apps/job.go
@@ -29,6 +29,7 @@ import (
 	batchinternal "k8s.io/kubernetes/pkg/apis/batch"
 	"k8s.io/kubernetes/test/e2e/framework"
 	jobutil "k8s.io/kubernetes/test/e2e/framework/job"
+	e2enode "k8s.io/kubernetes/test/e2e/framework/node"
 	e2epod "k8s.io/kubernetes/test/e2e/framework/pod"
 
 	"github.com/onsi/ginkgo"
@@ -97,12 +98,10 @@ var _ = SIGDescribe("Job", func() {
 	framework.ConformanceIt("should run a job to completion when tasks sometimes fail and are locally restarted", func() {
 		ginkgo.By("Creating a job")
 		// One failure, then a success, local restarts.
-		// We can't use the random failure approach used by the
-		// non-local test below, because kubelet will throttle
-		// frequently failing containers in a given pod, ramping
-		// up to 5 minutes between restarts, making test timeouts
-		// due to successive failures too likely with a reasonable
-		// test timeout.
+		// We can't use the random failure approach, because kubelet will
+		// throttle frequently failing containers in a given pod, ramping
+		// up to 5 minutes between restarts, making test timeout due to
+		// successive failures too likely with a reasonable test timeout.
 		job := jobutil.NewTestJob("failOnce", "fail-once-local", v1.RestartPolicyOnFailure, parallelism, completions, nil, backoffLimit)
 		job, err := jobutil.CreateJob(f.ClientSet, f.Namespace.Name, job)
 		framework.ExpectNoError(err, "failed to create job in namespace: %s", f.Namespace.Name)
@@ -114,18 +113,20 @@ var _ = SIGDescribe("Job", func() {
 
 	// Pods sometimes fail, but eventually succeed, after pod restarts
 	ginkgo.It("should run a job to completion when tasks sometimes fail and are not locally restarted", func() {
+		// One failure, then a success, no local restarts.
+		// We can't use the random failure approach, because JobController
+		// will throttle frequently failing Pods of a given Job, ramping
+		// up to 6 minutes between restarts, making test timeout due to
+		// successive failures.
+		// Instead, we force the Job's Pods to be scheduled to a single Node
+		// and use a hostPath volume to persist data across new Pods.
+		ginkgo.By("Looking for a node to schedule job pod")
+		node, err := e2enode.GetRandomReadySchedulableNode(f.ClientSet)
+		framework.ExpectNoError(err)
+
 		ginkgo.By("Creating a job")
-		// 50% chance of container success, local restarts.
-		// Can't use the failOnce approach because that relies
-		// on an emptyDir, which is not preserved across new pods.
-		// Worst case analysis: 15 failures, each taking 1 minute to
-		// run due to some slowness, 1 in 2^15 chance of happening,
-		// causing test flake.  Should be very rare.
-		// With the introduction of backoff limit and high failure rate this
-		// is hitting its timeout, the 3 is a reasonable that should make this
-		// test less flaky, for now.
-		job := jobutil.NewTestJob("randomlySucceedOrFail", "rand-non-local", v1.RestartPolicyNever, parallelism, 3, nil, 999)
-		job, err := jobutil.CreateJob(f.ClientSet, f.Namespace.Name, job)
+		job := jobutil.NewTestJobOnNode("failOnce", "fail-once-non-local", v1.RestartPolicyNever, parallelism, completions, nil, backoffLimit, node.Name)
+		job, err = jobutil.CreateJob(f.ClientSet, f.Namespace.Name, job)
 		framework.ExpectNoError(err, "failed to create job in namespace: %s", f.Namespace.Name)
 
 		ginkgo.By("Ensuring job reaches completions")
diff --git a/test/e2e/framework/job/BUILD b/test/e2e/framework/job/BUILD
index e799bd082a8..e635a7ee0d6 100644
--- a/test/e2e/framework/job/BUILD
+++ b/test/e2e/framework/job/BUILD
@@ -17,6 +17,7 @@ go_library(
         "//staging/src/k8s.io/apimachinery/pkg/api/errors:go_default_library",
         "//staging/src/k8s.io/apimachinery/pkg/apis/meta/v1:go_default_library",
         "//staging/src/k8s.io/apimachinery/pkg/labels:go_default_library",
+        "//staging/src/k8s.io/apimachinery/pkg/util/rand:go_default_library",
         "//staging/src/k8s.io/apimachinery/pkg/util/wait:go_default_library",
         "//staging/src/k8s.io/client-go/kubernetes:go_default_library",
         "//test/e2e/framework:go_default_library",
diff --git a/test/e2e/framework/job/fixtures.go b/test/e2e/framework/job/fixtures.go
index e6f13cc56bf..0ee29bd1d05 100644
--- a/test/e2e/framework/job/fixtures.go
+++ b/test/e2e/framework/job/fixtures.go
@@ -20,6 +20,7 @@ import (
 	batchv1 "k8s.io/api/batch/v1"
 	"k8s.io/api/core/v1"
 	metav1 "k8s.io/apimachinery/pkg/apis/meta/v1"
+	"k8s.io/apimachinery/pkg/util/rand"
 	"k8s.io/kubernetes/test/e2e/framework"
 )
 
@@ -30,6 +31,13 @@ import (
 // policy of the containers in which the Pod is running. Parallelism is the Job's parallelism, and completions is the
 // Job's required number of completions.
 func NewTestJob(behavior, name string, rPol v1.RestartPolicy, parallelism, completions int32, activeDeadlineSeconds *int64, backoffLimit int32) *batchv1.Job {
+	anyNode := ""
+	return NewTestJobOnNode(behavior, name, rPol, parallelism, completions, activeDeadlineSeconds, backoffLimit, anyNode)
+}
+
+// NewTestJobOnNode is similar to NewTestJob but supports specifying a Node on which the Job's Pods will run.
+// Empty nodeName means no node selection constraints.
+func NewTestJobOnNode(behavior, name string, rPol v1.RestartPolicy, parallelism, completions int32, activeDeadlineSeconds *int64, backoffLimit int32, nodeName string) *batchv1.Job {
 	manualSelector := false
 	job := &batchv1.Job{
 		ObjectMeta: metav1.ObjectMeta{
@@ -72,6 +80,7 @@ func NewTestJob(behavior, name string, rPol v1.RestartPolicy, parallelism, compl
 							SecurityContext: &v1.SecurityContext{},
 						},
 					},
+					NodeName: nodeName,
 				},
 			},
 		},
@@ -89,10 +98,21 @@ func NewTestJob(behavior, name string, rPol v1.RestartPolicy, parallelism, compl
 		job.Spec.Template.Spec.Containers[0].Command = []string{"/bin/sh", "-c", "exit $(( $RANDOM / 16384 ))"}
 	case "failOnce":
 		// Fail the first the container of the pod is run, and
-		// succeed the second time. Checks for file on emptydir.
+		// succeed the second time. Checks for file on a data volume.
 		// If present, succeed.  If not, create but fail.
-		// Note that this cannot be used with RestartNever because
-		// it always fails the first time for a pod.
+		// If RestartPolicy is Never, the nodeName should be set to
+		// ensure all job pods run on a single node and the volume
+		// will be mounted from a hostPath instead.
+		if len(nodeName) > 0 {
+			randomDir := "/tmp/job-e2e/" + rand.String(10)
+			hostPathType := v1.HostPathDirectoryOrCreate
+			job.Spec.Template.Spec.Volumes[0].VolumeSource = v1.VolumeSource{HostPath: &v1.HostPathVolumeSource{Path: randomDir, Type: &hostPathType}}
+			// Tests involving r/w operations on hostPath volume needs to run in
+			// privileged mode for SELinux enabled distro, while Windows platform
+			// neither supports nor needs privileged mode.
+			privileged := !framework.NodeOSDistroIs("windows")
+			job.Spec.Template.Spec.Containers[0].SecurityContext.Privileged = &privileged
+		}
 		job.Spec.Template.Spec.Containers[0].Command = []string{"/bin/sh", "-c", "if [[ -r /data/foo ]] ; then exit 0 ; else touch /data/foo ; exit 1 ; fi"}
 	}
 	return job