diff --git a/credentials/alts/internal/conn/aes128gcm.go b/credentials/alts/internal/conn/aes128gcm.go
index 04e0adb6c908..efd2a9f1feff 100644
--- a/credentials/alts/internal/conn/aes128gcm.go
+++ b/credentials/alts/internal/conn/aes128gcm.go
@@ -28,7 +28,7 @@ import (
 const (
 	// Overflow length n in bytes, never encrypt more than 2^(n*8) frames (in
 	// each direction).
-	overflowLenAES128GCM = 5
+	overflowLenAES128GCM = 4
 )
 
 // aes128gcm is the struct that holds necessary information for ALTS record.
diff --git a/credentials/alts/internal/conn/aes128gcmrekey.go b/credentials/alts/internal/conn/aes128gcmrekey.go
index 6a9035ea254f..84ec374ebb7e 100644
--- a/credentials/alts/internal/conn/aes128gcmrekey.go
+++ b/credentials/alts/internal/conn/aes128gcmrekey.go
@@ -27,7 +27,7 @@ import (
 const (
 	// Overflow length n in bytes, never encrypt more than 2^(n*8) frames (in
 	// each direction).
-	overflowLenAES128GCMRekey = 8
+	overflowLenAES128GCMRekey = 4
 	nonceLen                  = 12
 	aeadKeyLen                = 16
 	kdfKeyLen                 = 32
diff --git a/credentials/alts/internal/conn/counter_test.go b/credentials/alts/internal/conn/counter_test.go
index 0e752c3bfdde..2c9fc0f4d813 100644
--- a/credentials/alts/internal/conn/counter_test.go
+++ b/credentials/alts/internal/conn/counter_test.go
@@ -52,8 +52,9 @@ func (s) TestCounterSides(t *testing.T) {
 
 func (s) TestCounterInc(t *testing.T) {
 	for _, test := range []struct {
-		counter []byte
-		want    []byte
+		counter       []byte
+		want          []byte
+		expectInvalid bool
 	}{
 		{
 			counter: []byte{0x00, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
@@ -72,19 +73,32 @@ func (s) TestCounterInc(t *testing.T) {
 			want:    []byte{0x43, 0xff, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 		},
 		{
-			counter: []byte{0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
-			want:    []byte{0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+			counter: []byte{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+			want:    []byte{0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
 		},
 		{
-			counter: []byte{0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80},
-			want:    []byte{0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80},
+			counter: []byte{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80},
+			want:    []byte{0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80},
+		},
+		{
+			counter:       []byte{0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+			want:          []byte{},
+			expectInvalid: true,
+		},
+		{
+			counter:       []byte{0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80},
+			want:          []byte{},
+			expectInvalid: true,
 		},
 	} {
 		c := CounterFromValue(test.counter, overflowLenAES128GCM)
 		c.Inc()
 		value, _ := c.Value()
-		if g, w := value, test.want; !bytes.Equal(g, w) || c.invalid {
-			t.Errorf("counter(%v).Inc() =\n%v, want\n%v", test.counter, g, w)
+		if got, want := c.invalid, test.expectInvalid; got != want {
+			t.Errorf("counter.invalid=%t, want=%t", got, want)
+		}
+		if got, want := value, test.want; !bytes.Equal(got, want) {
+			t.Errorf("counter(%v).Inc() =\n%v, want\n%v", test.counter, got, want)
 		}
 	}
 }