diff --git a/pkg/controller/deployment/util/deployment_util.go b/pkg/controller/deployment/util/deployment_util.go
index bdb69886ff2..9b0ba5ebffc 100644
--- a/pkg/controller/deployment/util/deployment_util.go
+++ b/pkg/controller/deployment/util/deployment_util.go
@@ -410,7 +410,7 @@ func SetReplicasAnnotations(rs *extensions.ReplicaSet, desiredReplicas, maxRepli
 
 // MaxUnavailable returns the maximum unavailable pods a rolling deployment can take.
 func MaxUnavailable(deployment extensions.Deployment) int32 {
-	if !IsRollingUpdate(&deployment) {
+	if !IsRollingUpdate(&deployment) || *(deployment.Spec.Replicas) == 0 {
 		return int32(0)
 	}
 	// Error caught by validation
@@ -828,12 +828,12 @@ func IsRollingUpdate(deployment *extensions.Deployment) bool {
 	return deployment.Spec.Strategy.Type == extensions.RollingUpdateDeploymentStrategyType
 }
 
-// DeploymentComplete considers a deployment to be complete once its desired replicas equals its
-// updatedReplicas, no old pods are running, and it doesn't violate minimum availability.
+// DeploymentComplete considers a deployment to be complete once all of its desired replicas
+// are updated and available, and no old pods are running.
 func DeploymentComplete(deployment *extensions.Deployment, newStatus *extensions.DeploymentStatus) bool {
 	return newStatus.UpdatedReplicas == *(deployment.Spec.Replicas) &&
 		newStatus.Replicas == *(deployment.Spec.Replicas) &&
-		newStatus.AvailableReplicas >= *(deployment.Spec.Replicas)-MaxUnavailable(*deployment) &&
+		newStatus.AvailableReplicas == *(deployment.Spec.Replicas) &&
 		newStatus.ObservedGeneration >= deployment.Generation
 }
 
diff --git a/pkg/controller/deployment/util/deployment_util_test.go b/pkg/controller/deployment/util/deployment_util_test.go
index 18869302880..9e5615b3d92 100644
--- a/pkg/controller/deployment/util/deployment_util_test.go
+++ b/pkg/controller/deployment/util/deployment_util_test.go
@@ -960,37 +960,43 @@ func TestDeploymentComplete(t *testing.T) {
 		expected bool
 	}{
 		{
-			name: "complete",
+			name: "not complete: min but not all pods become available",
 
 			d:        deployment(5, 5, 5, 4, 1, 0),
-			expected: true,
+			expected: false,
 		},
 		{
-			name: "not complete",
+			name: "not complete: min availability is not honored",
 
 			d:        deployment(5, 5, 5, 3, 1, 0),
 			expected: false,
 		},
 		{
-			name: "complete #2",
+			name: "complete",
 
 			d:        deployment(5, 5, 5, 5, 0, 0),
 			expected: true,
 		},
 		{
-			name: "not complete #2",
+			name: "not complete: all pods are available but not updated",
 
 			d:        deployment(5, 5, 4, 5, 0, 0),
 			expected: false,
 		},
 		{
-			name: "not complete #3",
+			name: "not complete: still running old pods",
 
 			// old replica set: spec.replicas=1, status.replicas=1, status.availableReplicas=1
 			// new replica set: spec.replicas=1, status.replicas=1, status.availableReplicas=0
 			d:        deployment(1, 2, 1, 1, 0, 1),
 			expected: false,
 		},
+		{
+			name: "not complete: one replica deployment never comes up",
+
+			d:        deployment(1, 1, 1, 0, 1, 1),
+			expected: false,
+		},
 	}
 
 	for _, test := range tests {