diff --git a/plugin/dns64/README.md b/plugin/dns64/README.md
index 39c9cf757..dc2cf86f0 100644
--- a/plugin/dns64/README.md
+++ b/plugin/dns64/README.md
@@ -20,6 +20,8 @@ dns64 [PREFIX]
 ~~~
 
 * **PREFIX** defines a custom prefix instead of the default `64:ff9b::/96`.
+  Its length must be 32, 40, 48, 56, 64, or 96 bits, as defined in
+  [RFC 6052 Section 2.2](https://www.rfc-editor.org/info/rfc6052/#section-2.2).
 
 Or use this slightly longer form with more options:
 
diff --git a/plugin/dns64/setup.go b/plugin/dns64/setup.go
index 5e061875f..8c46973c5 100644
--- a/plugin/dns64/setup.go
+++ b/plugin/dns64/setup.go
@@ -84,7 +84,9 @@ func parsePrefix(c *caddy.Controller, addr string) (*net.IPNet, error) {
 	if total != 128 {
 		return nil, c.Errf("invalid netmask %d IPv6 address: %q", total, pref)
 	}
-	if n%8 != 0 || n < 32 || n > 96 {
+	switch n {
+	case 32, 40, 48, 56, 64, 96:
+	default:
 		return nil, c.Errf("invalid prefix length %q", pref)
 	}
 
diff --git a/plugin/dns64/setup_test.go b/plugin/dns64/setup_test.go
index e7d13f418..fd1d7d58f 100644
--- a/plugin/dns64/setup_test.go
+++ b/plugin/dns64/setup_test.go
@@ -1,11 +1,31 @@
 package dns64
 
 import (
+	"fmt"
 	"testing"
 
 	"github.com/coredns/caddy"
 )
 
+func TestSetupDns64PrefixLengths(t *testing.T) {
+	for _, length := range []int{32, 40, 48, 56, 64, 72, 80, 88, 96} {
+		prefix := fmt.Sprintf("2001:db8::/%d", length)
+		for _, input := range []string{
+			"dns64 " + prefix,
+			"dns64 {\n prefix " + prefix + "\n}",
+		} {
+			t.Run(input, func(t *testing.T) {
+				c := caddy.NewTestController("dns", input)
+				_, err := dns64Parse(c)
+				invalid := length == 72 || length == 80 || length == 88
+				if (err != nil) != invalid {
+					t.Errorf("prefix /%d: expected error %v, got %v", length, invalid, err)
+				}
+			})
+		}
+	}
+}
+
 func TestSetupDns64(t *testing.T) {
 	tests := []struct {
 		inputUpstreams string