diff --git a/staging/src/k8s.io/pod-security-admission/policy/check_privileged.go b/staging/src/k8s.io/pod-security-admission/policy/check_privileged.go
index 20fafa3bb1e..6824cf8d8bc 100644
--- a/staging/src/k8s.io/pod-security-admission/policy/check_privileged.go
+++ b/staging/src/k8s.io/pod-security-admission/policy/check_privileged.go
@@ -17,7 +17,7 @@ limitations under the License.
 package policy
 
 import (
-	"strings"
+	"fmt"
 
 	corev1 "k8s.io/api/core/v1"
 	metav1 "k8s.io/apimachinery/pkg/apis/meta/v1"
@@ -32,7 +32,7 @@ Restricted Fields:
 spec.containers[*].securityContext.privileged
 spec.initContainers[*].securityContext.privileged
 
-Allowed Values: false, undefined/nil
+Allowed Values: false, undefined/null
 */
 
 func init() {
@@ -40,7 +40,7 @@ func init() {
 }
 
 // CheckPrivileged returns a baseline level check
-// that requires privileged=false in 1.0+
+// that forbids privileged=true in 1.0+
 func CheckPrivileged() Check {
 	return Check{
 		ID:    "privileged",
@@ -55,17 +55,21 @@ func CheckPrivileged() Check {
 }
 
 func privileged_1_0(podMetadata *metav1.ObjectMeta, podSpec *corev1.PodSpec) CheckResult {
-	var forbiddenPaths []string
+	var badContainers []string
 	visitContainersWithPath(podSpec, field.NewPath("spec"), func(container *corev1.Container, path *field.Path) {
 		if container.SecurityContext != nil && container.SecurityContext.Privileged != nil && *container.SecurityContext.Privileged {
-			forbiddenPaths = append(forbiddenPaths, path.Child("securityContext", "privileged").String())
+			badContainers = append(badContainers, container.Name)
 		}
 	})
-	if len(forbiddenPaths) > 0 {
+	if len(badContainers) > 0 {
 		return CheckResult{
 			Allowed:         false,
-			ForbiddenReason: "privileged == true",
-			ForbiddenDetail: strings.Join(forbiddenPaths, ", "),
+			ForbiddenReason: "privileged",
+			ForbiddenDetail: fmt.Sprintf(
+				`%s %s must not set securityContext.privileged=true`,
+				pluralize("container", "containers", len(badContainers)),
+				joinQuote(badContainers),
+			),
 		}
 	}
 	return CheckResult{Allowed: true}
diff --git a/staging/src/k8s.io/pod-security-admission/policy/check_privileged_test.go b/staging/src/k8s.io/pod-security-admission/policy/check_privileged_test.go
new file mode 100644
index 00000000000..ed469620ebb
--- /dev/null
+++ b/staging/src/k8s.io/pod-security-admission/policy/check_privileged_test.go
@@ -0,0 +1,63 @@
+/*
+Copyright 2021 The Kubernetes Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+package policy
+
+import (
+	"testing"
+
+	corev1 "k8s.io/api/core/v1"
+	utilpointer "k8s.io/utils/pointer"
+)
+
+func TestPrivileged(t *testing.T) {
+	tests := []struct {
+		name         string
+		pod          *corev1.Pod
+		expectReason string
+		expectDetail string
+	}{
+		{
+			name: "privileged",
+			pod: &corev1.Pod{Spec: corev1.PodSpec{
+				Containers: []corev1.Container{
+					{Name: "a", SecurityContext: nil},
+					{Name: "b", SecurityContext: &corev1.SecurityContext{}},
+					{Name: "c", SecurityContext: &corev1.SecurityContext{Privileged: utilpointer.Bool(false)}},
+					{Name: "d", SecurityContext: &corev1.SecurityContext{Privileged: utilpointer.Bool(true)}},
+					{Name: "e", SecurityContext: &corev1.SecurityContext{Privileged: utilpointer.Bool(true)}},
+				},
+			}},
+			expectReason: `privileged`,
+			expectDetail: `containers "d", "e" must not set securityContext.privileged=true`,
+		},
+	}
+
+	for _, tc := range tests {
+		t.Run(tc.name, func(t *testing.T) {
+			result := privileged_1_0(&tc.pod.ObjectMeta, &tc.pod.Spec)
+			if result.Allowed {
+				t.Fatal("expected disallowed")
+			}
+			if e, a := tc.expectReason, result.ForbiddenReason; e != a {
+				t.Errorf("expected\n%s\ngot\n%s", e, a)
+			}
+			if e, a := tc.expectDetail, result.ForbiddenDetail; e != a {
+				t.Errorf("expected\n%s\ngot\n%s", e, a)
+			}
+		})
+	}
+}
diff --git a/staging/src/k8s.io/pod-security-admission/test/fixtures_privileged.go b/staging/src/k8s.io/pod-security-admission/test/fixtures_privileged.go
index ffac5e3a45c..babdcf6ba65 100644
--- a/staging/src/k8s.io/pod-security-admission/test/fixtures_privileged.go
+++ b/staging/src/k8s.io/pod-security-admission/test/fixtures_privileged.go
@@ -36,7 +36,7 @@ func init() {
 		generatePass: func(p *corev1.Pod) []*corev1.Pod {
 			p = ensureSecurityContext(p)
 			return []*corev1.Pod{
-				// privileged set to false
+				// privileged explicitly set to false
 				tweak(p, func(p *corev1.Pod) {
 					p.Spec.Containers[0].SecurityContext.Privileged = pointer.BoolPtr(false)
 					p.Spec.InitContainers[0].SecurityContext.Privileged = pointer.BoolPtr(false)