diff --git a/backend/crypt/cipher.go b/backend/crypt/cipher.go
index 77dc34643..470da07a0 100644
--- a/backend/crypt/cipher.go
+++ b/backend/crypt/cipher.go
@@ -12,12 +12,14 @@ import (
 	"strconv"
 	"strings"
 	"sync"
+	"time"
 	"unicode/utf8"
 
 	"github.com/pkg/errors"
 	"github.com/rclone/rclone/backend/crypt/pkcs7"
 	"github.com/rclone/rclone/fs"
 	"github.com/rclone/rclone/fs/accounting"
+	"github.com/rclone/rclone/lib/version"
 	"github.com/rfjakob/eme"
 	"golang.org/x/crypto/nacl/secretbox"
 	"golang.org/x/crypto/scrypt"
@@ -442,11 +444,32 @@ func (c *Cipher) encryptFileName(in string) string {
 		if !c.dirNameEncrypt && i != (len(segments)-1) {
 			continue
 		}
+
+		// Strip version string so that only the non-versioned part
+		// of the file name gets encrypted/obfuscated
+		hasVersion := false
+		var t time.Time
+		if 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]
+			if s != segments[i] {
+				segments[i] = s
+				hasVersion = true
+			}
+		}
+
 		if c.mode == NameEncryptionStandard {
 			segments[i] = c.encryptSegment(segments[i])
 		} else {
 			segments[i] = c.obfuscateSegment(segments[i])
 		}
+
+		// Add back a version to the encrypted/obfuscated
+		// file name, if we stripped it off earlier
+		if hasVersion {
+			segments[i] = version.Add(segments[i], t)
+		}
 	}
 	return strings.Join(segments, "/")
 }
@@ -477,6 +500,21 @@ func (c *Cipher) decryptFileName(in string) (string, error) {
 		if !c.dirNameEncrypt && i != (len(segments)-1) {
 			continue
 		}
+
+		// Strip version string so that only the non-versioned part
+		// of the file name gets decrypted/deobfuscated
+		hasVersion := false
+		var t time.Time
+		if 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]
+			if s != segments[i] {
+				segments[i] = s
+				hasVersion = true
+			}
+		}
+
 		if c.mode == NameEncryptionStandard {
 			segments[i], err = c.decryptSegment(segments[i])
 		} else {
@@ -486,6 +524,12 @@ func (c *Cipher) decryptFileName(in string) (string, error) {
 		if err != nil {
 			return "", err
 		}
+
+		// Add back a version to the decrypted/deobfuscated
+		// file name, if we stripped it off earlier
+		if hasVersion {
+			segments[i] = version.Add(segments[i], t)
+		}
 	}
 	return strings.Join(segments, "/"), nil
 }
@@ -494,10 +538,18 @@ func (c *Cipher) decryptFileName(in string) (string, error) {
 func (c *Cipher) DecryptFileName(in string) (string, error) {
 	if c.mode == NameEncryptionOff {
 		remainingLength := len(in) - len(encryptedSuffix)
-		if remainingLength > 0 && strings.HasSuffix(in, encryptedSuffix) {
-			return in[:remainingLength], nil
+		if remainingLength == 0 || !strings.HasSuffix(in, encryptedSuffix) {
+			return "", ErrorNotAnEncryptedFile
 		}
-		return "", ErrorNotAnEncryptedFile
+		decrypted := in[:remainingLength]
+		if version.Match(decrypted) {
+			_, unversioned := version.Remove(decrypted)
+			if unversioned == "" {
+				return "", ErrorNotAnEncryptedFile
+			}
+		}
+		// Leave the version string on, if it was there
+		return decrypted, nil
 	}
 	return c.decryptFileName(in)
 }
diff --git a/backend/crypt/cipher_test.go b/backend/crypt/cipher_test.go
index ff9bb23c5..dbe0e42be 100644
--- a/backend/crypt/cipher_test.go
+++ b/backend/crypt/cipher_test.go
@@ -160,22 +160,29 @@ func TestEncryptFileName(t *testing.T) {
 	assert.Equal(t, "p0e52nreeaj0a5ea7s64m4j72s", c.EncryptFileName("1"))
 	assert.Equal(t, "p0e52nreeaj0a5ea7s64m4j72s/l42g6771hnv3an9cgc8cr2n1ng", c.EncryptFileName("1/12"))
 	assert.Equal(t, "p0e52nreeaj0a5ea7s64m4j72s/l42g6771hnv3an9cgc8cr2n1ng/qgm4avr35m5loi1th53ato71v0", c.EncryptFileName("1/12/123"))
+	assert.Equal(t, "p0e52nreeaj0a5ea7s64m4j72s-v2001-02-03-040506-123", c.EncryptFileName("1-v2001-02-03-040506-123"))
+	assert.Equal(t, "p0e52nreeaj0a5ea7s64m4j72s/l42g6771hnv3an9cgc8cr2n1ng-v2001-02-03-040506-123", c.EncryptFileName("1/12-v2001-02-03-040506-123"))
 	// Standard mode with directory name encryption off
 	c, _ = newCipher(NameEncryptionStandard, "", "", false)
 	assert.Equal(t, "p0e52nreeaj0a5ea7s64m4j72s", c.EncryptFileName("1"))
 	assert.Equal(t, "1/l42g6771hnv3an9cgc8cr2n1ng", c.EncryptFileName("1/12"))
 	assert.Equal(t, "1/12/qgm4avr35m5loi1th53ato71v0", c.EncryptFileName("1/12/123"))
+	assert.Equal(t, "p0e52nreeaj0a5ea7s64m4j72s-v2001-02-03-040506-123", c.EncryptFileName("1-v2001-02-03-040506-123"))
+	assert.Equal(t, "1/l42g6771hnv3an9cgc8cr2n1ng-v2001-02-03-040506-123", c.EncryptFileName("1/12-v2001-02-03-040506-123"))
 	// Now off mode
 	c, _ = newCipher(NameEncryptionOff, "", "", true)
 	assert.Equal(t, "1/12/123.bin", c.EncryptFileName("1/12/123"))
 	// Obfuscation mode
 	c, _ = newCipher(NameEncryptionObfuscated, "", "", true)
 	assert.Equal(t, "49.6/99.23/150.890/53.!!lipps", c.EncryptFileName("1/12/123/!hello"))
+	assert.Equal(t, "49.6/99.23/150.890/53-v2001-02-03-040506-123.!!lipps", c.EncryptFileName("1/12/123/!hello-v2001-02-03-040506-123"))
+	assert.Equal(t, "49.6/99.23/150.890/162.uryyB-v2001-02-03-040506-123.GKG", c.EncryptFileName("1/12/123/hello-v2001-02-03-040506-123.txt"))
 	assert.Equal(t, "161.\u00e4", c.EncryptFileName("\u00a1"))
 	assert.Equal(t, "160.\u03c2", c.EncryptFileName("\u03a0"))
 	// Obfuscation mode with directory name encryption off
 	c, _ = newCipher(NameEncryptionObfuscated, "", "", false)
 	assert.Equal(t, "1/12/123/53.!!lipps", c.EncryptFileName("1/12/123/!hello"))
+	assert.Equal(t, "1/12/123/53-v2001-02-03-040506-123.!!lipps", c.EncryptFileName("1/12/123/!hello-v2001-02-03-040506-123"))
 	assert.Equal(t, "161.\u00e4", c.EncryptFileName("\u00a1"))
 	assert.Equal(t, "160.\u03c2", c.EncryptFileName("\u03a0"))
 }
@@ -194,14 +201,19 @@ func TestDecryptFileName(t *testing.T) {
 		{NameEncryptionStandard, true, "p0e52nreeaj0a5ea7s64m4j72s/l42g6771hnv3an9cgc8cr2n1ng/qgm4avr35m5loi1th53ato71v0", "1/12/123", nil},
 		{NameEncryptionStandard, true, "p0e52nreeaj0a5ea7s64m4j72s/l42g6771hnv3an9cgc8cr2n1/qgm4avr35m5loi1th53ato71v0", "", ErrorNotAMultipleOfBlocksize},
 		{NameEncryptionStandard, false, "1/12/qgm4avr35m5loi1th53ato71v0", "1/12/123", nil},
+		{NameEncryptionStandard, true, "p0e52nreeaj0a5ea7s64m4j72s-v2001-02-03-040506-123", "1-v2001-02-03-040506-123", nil},
 		{NameEncryptionOff, true, "1/12/123.bin", "1/12/123", nil},
 		{NameEncryptionOff, true, "1/12/123.bix", "", ErrorNotAnEncryptedFile},
 		{NameEncryptionOff, true, ".bin", "", ErrorNotAnEncryptedFile},
+		{NameEncryptionOff, true, "1/12/123-v2001-02-03-040506-123.bin", "1/12/123-v2001-02-03-040506-123", nil},
+		{NameEncryptionOff, true, "1/12/123-v1970-01-01-010101-123-v2001-02-03-040506-123.bin", "1/12/123-v1970-01-01-010101-123-v2001-02-03-040506-123", nil},
+		{NameEncryptionOff, true, "1/12/123-v1970-01-01-010101-123-v2001-02-03-040506-123.txt.bin", "1/12/123-v1970-01-01-010101-123-v2001-02-03-040506-123.txt", nil},
 		{NameEncryptionObfuscated, true, "!.hello", "hello", nil},
 		{NameEncryptionObfuscated, true, "hello", "", ErrorNotAnEncryptedFile},
 		{NameEncryptionObfuscated, true, "161.\u00e4", "\u00a1", nil},
 		{NameEncryptionObfuscated, true, "160.\u03c2", "\u03a0", nil},
 		{NameEncryptionObfuscated, false, "1/12/123/53.!!lipps", "1/12/123/!hello", nil},
+		{NameEncryptionObfuscated, false, "1/12/123/53-v2001-02-03-040506-123.!!lipps", "1/12/123/!hello-v2001-02-03-040506-123", nil},
 	} {
 		c, _ := newCipher(test.mode, "", "", test.dirNameEncrypt)
 		actual, actualErr := c.DecryptFileName(test.in)
diff --git a/docs/content/b2.md b/docs/content/b2.md
index 427935b1e..4967f7415 100644
--- a/docs/content/b2.md
+++ b/docs/content/b2.md
@@ -172,11 +172,6 @@ the file instead of hiding it.
 Old versions of files, where available, are visible using the 
 `--b2-versions` flag.
 
-**NB** Note that `--b2-versions` does not work with crypt at the
-moment [#1627](https://github.com/rclone/rclone/issues/1627). Using
-[--backup-dir](/docs/#backup-dir-dir) with rclone is the recommended
-way of working around this.
-
 If you wish to remove all the old versions then you can use the
 `rclone cleanup remote:bucket` command which will delete all the old
 versions of files, leaving the current ones intact.  You can also