diff --git a/backend/crypt/cipher.go b/backend/crypt/cipher.go
index 6f4c987f6..d05a93924 100644
--- a/backend/crypt/cipher.go
+++ b/backend/crypt/cipher.go
@@ -486,7 +486,14 @@ func (c *Cipher) deobfuscateSegment(ciphertext string) (string, error) {
 }
 
 // encryptFileName encrypts a file path
-func (c *Cipher) encryptFileName(in string) string {
+//
+// If stripVersion is set then a version string on the last segment (as
+// used by --b2-versions) is removed before encryption and put back in
+// plain text afterwards. Only file leaf names are given version strings
+// by the underlying backend, so it must not be set for directory names,
+// which would otherwise encrypt differently from the same directory
+// appearing as the parent of a file name.
+func (c *Cipher) encryptFileName(in string, stripVersion bool) string {
 	segments := strings.Split(in, "/")
 	for i := range segments {
 		// Skip directory name encryption if the user chose to
@@ -499,7 +506,7 @@ func (c *Cipher) encryptFileName(in string) string {
 		// of the file name gets encrypted/obfuscated
 		hasVersion := false
 		var t time.Time
-		if i == (len(segments)-1) && version.Match(segments[i]) {
+		if stripVersion && i == (len(segments)-1) && version.Match(segments[i]) {
 			var s string
 			t, s = version.Remove(segments[i])
 			// version.Remove can fail, in which case it returns segments[i]
@@ -529,7 +536,7 @@ func (c *Cipher) EncryptFileName(in string) string {
 	if c.mode == NameEncryptionOff {
 		return in + c.encryptedSuffix
 	}
-	return c.encryptFileName(in)
+	return c.encryptFileName(in, true)
 }
 
 // EncryptDirName encrypts a directory path
@@ -537,11 +544,13 @@ func (c *Cipher) EncryptDirName(in string) string {
 	if c.mode == NameEncryptionOff || !c.dirNameEncrypt {
 		return in
 	}
-	return c.encryptFileName(in)
+	return c.encryptFileName(in, false)
 }
 
 // decryptFileName decrypts a file path
-func (c *Cipher) decryptFileName(in string) (string, error) {
+//
+// stripVersion is as for encryptFileName.
+func (c *Cipher) decryptFileName(in string, stripVersion bool) (string, error) {
 	segments := strings.Split(in, "/")
 	for i := range segments {
 		var err error
@@ -555,7 +564,7 @@ func (c *Cipher) decryptFileName(in string) (string, error) {
 		// of the file name gets decrypted/deobfuscated
 		hasVersion := false
 		var t time.Time
-		if i == (len(segments)-1) && version.Match(segments[i]) {
+		if stripVersion && i == (len(segments)-1) && version.Match(segments[i]) {
 			var s string
 			t, s = version.Remove(segments[i])
 			// version.Remove can fail, in which case it returns segments[i]
@@ -601,7 +610,7 @@ func (c *Cipher) DecryptFileName(in string) (string, error) {
 		// Leave the version string on, if it was there
 		return decrypted, nil
 	}
-	return c.decryptFileName(in)
+	return c.decryptFileName(in, true)
 }
 
 // DecryptDirName decrypts a directory path
@@ -609,7 +618,7 @@ func (c *Cipher) DecryptDirName(in string) (string, error) {
 	if c.mode == NameEncryptionOff || !c.dirNameEncrypt {
 		return in, nil
 	}
-	return c.decryptFileName(in)
+	return c.decryptFileName(in, false)
 }
 
 // NameEncryptionMode returns the encryption mode in use for names
diff --git a/backend/crypt/cipher_test.go b/backend/crypt/cipher_test.go
index fe2edc6f9..217b85447 100644
--- a/backend/crypt/cipher_test.go
+++ b/backend/crypt/cipher_test.go
@@ -682,6 +682,28 @@ func TestNonStandardDecryptDirName(t *testing.T) {
 	}
 }
 
+// Test directories whose name looks like it has a version string -
+// these encrypt verbatim, so that EncryptDirName agrees with the same
+// directory encrypted as the parent of a file name
+func TestVersionedDirName(t *testing.T) {
+	const dir = "dir-v2001-02-03-040506-123"
+	for _, encoding := range []string{"base32", "base64", "base32768"} {
+		enc, _ := NewNameEncoding(encoding)
+		for _, mode := range []NameEncryptionMode{NameEncryptionStandard, NameEncryptionObfuscated} {
+			c, _ := newCipher(mode, "", "", true, enc)
+			what := fmt.Sprintf("Testing %q (mode=%v)", encoding, mode)
+			// Check EncryptDirName matches the parent of an encrypted file name
+			encryptedDir := c.EncryptDirName(dir)
+			encryptedFile := c.EncryptFileName(dir + "/file.txt")
+			assert.Equal(t, encryptedDir+"/", encryptedFile[:strings.LastIndex(encryptedFile, "/")+1], what)
+			// Check the encrypted directory name round trips OK
+			decryptedDir, err := c.DecryptDirName(encryptedDir)
+			assert.NoError(t, err, what)
+			assert.Equal(t, dir, decryptedDir, what)
+		}
+	}
+}
+
 func TestEncryptedSize(t *testing.T) {
 	c, _ := newCipher(NameEncryptionStandard, "", "", true, nil)
 	for _, test := range []struct {