diff --git a/backend/crypt/crypt.go b/backend/crypt/crypt.go
index 002fbc8cc..8b6d38ad4 100644
--- a/backend/crypt/crypt.go
+++ b/backend/crypt/crypt.go
@@ -1049,6 +1049,10 @@ func (o *ObjectInfo) Hash(ctx context.Context, hash hash.Type) (string, error) {
 	}
 	// if this is wrapping a local object then we work out the hash
 	if srcObj.Fs().Features().IsLocal {
+		if o.f.opt.NoDataEncryption {
+			// If no encryption, just return the hash of the underlying object
+			return srcObj.Hash(ctx, hash)
+		}
 		// Read the data and encrypt it to calculate the hash
 		fs.Debugf(o, "Computing %v hash of encrypted source", hash)
 		return o.f.computeHashWithNonce(ctx, o.nonce, srcObj, hash)
diff --git a/backend/crypt/crypt_internal_test.go b/backend/crypt/crypt_internal_test.go
index 2f7f1f8b3..62adb4952 100644
--- a/backend/crypt/crypt_internal_test.go
+++ b/backend/crypt/crypt_internal_test.go
@@ -77,7 +77,11 @@ func testObjectInfo(t *testing.T, f *Fs, wrap bool) {
 	enc, err := f.cipher.newEncrypter(inBuf, nil)
 	require.NoError(t, err)
 	nonce := enc.nonce // read the nonce at the start
-	_, err = io.Copy(&outBuf, enc)
+	if f.opt.NoDataEncryption {
+		_, err = outBuf.WriteString(contents)
+	} else {
+		_, err = io.Copy(&outBuf, enc)
+	}
 	require.NoError(t, err)
 
 	var oi fs.ObjectInfo = obj
@@ -96,7 +100,12 @@ func testObjectInfo(t *testing.T, f *Fs, wrap bool) {
 	assert.NotEqual(t, path, src.Remote())
 
 	// Test ObjectInfo.Hash
-	wantHash := md5.Sum(outBuf.Bytes())
+	var wantHash [md5.Size]byte
+	if f.opt.NoDataEncryption {
+		wantHash = md5.Sum([]byte(contents))
+	} else {
+		wantHash = md5.Sum(outBuf.Bytes())
+	}
 	gotHash, err := src.Hash(ctx, hash.MD5)
 	require.NoError(t, err)
 	assert.Equal(t, fmt.Sprintf("%x", wantHash), gotHash)