diff --git a/cmd/cmd.go b/cmd/cmd.go
index 6b6d52a49..89ddccadf 100644
--- a/cmd/cmd.go
+++ b/cmd/cmd.go
@@ -166,7 +166,11 @@ func NewFsSrcDst(args []string) (fs.Fs, fs.Fs) {
 
 // RemoteSplit splits a remote into a parent and a leaf
 //
-// if it returns parent as an empty string then it wasn't possible
+// if it returns leaf as an empty string then remote is a directory
+//
+// if it returns parent as an empty string then that means the current directory
+//
+// The returned values have the property that parent + leaf == remote
 func RemoteSplit(remote string) (parent string, leaf string) {
 	// Split remote on :
 	i := strings.Index(remote, ":")
@@ -175,23 +179,13 @@ func RemoteSplit(remote string) (parent string, leaf string) {
 	if i >= 0 {
 		remoteName = remote[:i+1]
 		remotePath = remote[i+1:]
-	}
-	if remotePath == "" {
-		return "", ""
+	} else if strings.HasSuffix(remotePath, "/") {
+		// if no : and ends with / must be directory
+		return remotePath, ""
 	}
 	// Construct new remote name without last segment
 	parent, leaf = path.Split(remotePath)
-	if leaf == "" {
-		return "", ""
-	}
-	if parent != "/" {
-		parent = strings.TrimSuffix(parent, "/")
-	}
-	parent = remoteName + parent
-	if parent == "" {
-		parent = "."
-	}
-	return parent, leaf
+	return remoteName + parent, leaf
 }
 
 // NewFsSrcDstFiles creates a new src and dst fs from the arguments
@@ -203,7 +197,10 @@ func NewFsSrcDstFiles(args []string) (fsrc fs.Fs, srcFileName string, fdst fs.Fs
 	if srcFileName != "" {
 		dstRemote, dstFileName = RemoteSplit(dstRemote)
 		if dstRemote == "" {
-			log.Fatalf("Can't find parent directory for %q", args[1])
+			dstRemote = "."
+		}
+		if dstFileName == "" {
+			log.Fatalf("%q is a directory", args[1])
 		}
 	}
 	fdst = newFsDst(dstRemote)
diff --git a/cmd/cmd_test.go b/cmd/cmd_test.go
index d8056ee8f..126350d9c 100644
--- a/cmd/cmd_test.go
+++ b/cmd/cmd_test.go
@@ -1,6 +1,7 @@
 package cmd
 
 import (
+	"fmt"
 	"testing"
 
 	"github.com/stretchr/testify/assert"
@@ -12,17 +13,23 @@ func TestRemoteSplit(t *testing.T) {
 		remote, wantParent, wantLeaf string
 	}{
 		{"", "", ""},
-		{"remote:", "", ""},
+		{"remote:", "remote:", ""},
 		{"remote:potato", "remote:", "potato"},
-		{"remote:potato/sausage", "remote:potato", "sausage"},
-		{"/", "", ""},
+		{"remote:/", "remote:/", ""},
+		{"remote:/potato", "remote:/", "potato"},
+		{"remote:/potato/potato", "remote:/potato/", "potato"},
+		{"remote:potato/sausage", "remote:potato/", "sausage"},
+		{"/", "/", ""},
 		{"/root", "/", "root"},
-		{"/a/b", "/a", "b"},
-		{"root", ".", "root"},
-		{"a/b", "a", "b"},
+		{"/a/b", "/a/", "b"},
+		{"root", "", "root"},
+		{"a/b", "a/", "b"},
+		{"root/", "root/", ""},
+		{"a/b/", "a/b/", ""},
 	} {
 		gotParent, gotLeaf := RemoteSplit(test.remote)
 		assert.Equal(t, test.wantParent, gotParent, test.remote)
 		assert.Equal(t, test.wantLeaf, gotLeaf, test.remote)
+		assert.Equal(t, test.remote, gotParent+gotLeaf, fmt.Sprintf("%s: %q + %q != %q", test.remote, gotParent, gotLeaf, test.remote))
 	}
 }