diff --git a/drive/driveimpl/compositedav/compositedav.go b/drive/driveimpl/compositedav/compositedav.go
index 9bcba158e..024f8be3b 100644
--- a/drive/driveimpl/compositedav/compositedav.go
+++ b/drive/driveimpl/compositedav/compositedav.go
@@ -100,7 +100,7 @@ func (h *Handler) ServeHTTP(w http.ResponseWriter, r *http.Request) {
 	pathComponents := shared.CleanAndSplit(r.URL.Path)
 
 	if len(pathComponents) >= mpl {
-		h.delegate(pathComponents[mpl-1:], w, r)
+		h.delegate(mpl, pathComponents[mpl-1:], w, r)
 		return
 	}
 	h.handle(w, r)
@@ -129,24 +129,41 @@ func (h *Handler) handle(w http.ResponseWriter, r *http.Request) {
 }
 
 // delegate sends the request to the Child WebDAV server.
-func (h *Handler) delegate(pathComponents []string, w http.ResponseWriter, r *http.Request) string {
+func (h *Handler) delegate(mpl int, pathComponents []string, w http.ResponseWriter, r *http.Request) {
+	dest := r.Header.Get("Destination")
+	if dest != "" {
+		// Rewrite destination header
+		destURL, err := url.Parse(dest)
+		if err != nil {
+			http.Error(w, err.Error(), http.StatusBadRequest)
+			return
+		}
+		destinationComponents := shared.CleanAndSplit(destURL.Path)
+		if len(destinationComponents) < mpl || destinationComponents[mpl-1] != pathComponents[0] {
+			http.Error(w, "Destination across shares is not supported", http.StatusBadRequest)
+			return
+		}
+		updatedDest := shared.JoinEscaped(destinationComponents[mpl:]...)
+		r.Header.Set("Destination", updatedDest)
+	}
+
 	childName := pathComponents[0]
 	child := h.GetChild(childName)
 	if child == nil {
 		w.WriteHeader(http.StatusNotFound)
-		return childName
+		return
 	}
+
 	u, err := url.Parse(child.BaseURL)
 	if err != nil {
 		h.logf("warning: parse base URL %s failed: %s", child.BaseURL, err)
 		http.Error(w, err.Error(), http.StatusInternalServerError)
-		return childName
+		return
 	}
 	u.Path = path.Join(u.Path, shared.Join(pathComponents[1:]...))
 	r.URL = u
 	r.Host = u.Host
 	child.rp.ServeHTTP(w, r)
-	return childName
 }
 
 // SetChildren replaces the entire existing set of children with the given
diff --git a/drive/driveimpl/compositedav/propfind.go b/drive/driveimpl/compositedav/propfind.go
index 868a1d2b2..60b90edb2 100644
--- a/drive/driveimpl/compositedav/propfind.go
+++ b/drive/driveimpl/compositedav/propfind.go
@@ -37,7 +37,7 @@ func (h *Handler) handlePROPFIND(w http.ResponseWriter, r *http.Request) {
 		bw := &bufferingResponseWriter{ResponseWriter: w}
 
 		mpl := h.maxPathLength(r)
-		h.delegate(pathComponents[mpl-1:], bw, r)
+		h.delegate(mpl, pathComponents[mpl-1:], bw, r)
 
 		// Fixup paths to add the requested path as a prefix.
 		pathPrefix := shared.Join(pathComponents[0:mpl]...)
diff --git a/drive/driveimpl/drive_test.go b/drive/driveimpl/drive_test.go
index 2f25cf50b..6dc4c7ce5 100644
--- a/drive/driveimpl/drive_test.go
+++ b/drive/driveimpl/drive_test.go
@@ -33,6 +33,7 @@
 	share11 = `sha re$%11`
 	share12 = `_sha re$%12`
 	file111 = `fi le$%111.txt`
+	file112 = `file112.txt`
 )
 
 func init() {
@@ -81,9 +82,13 @@ func TestFileManipulation(t *testing.T) {
 	s.checkFileStatus(remote1, share11, file111)
 	s.checkFileContents(remote1, share11, file111)
 
+	s.renameFile("renaming file across shares should fail", remote1, share11, file111, share12, file112, false)
+
+	s.renameFile("renaming file in same share should succeed", remote1, share11, file111, share11, file112, true)
+	s.checkFileContents(remote1, share11, file112)
+
 	s.addShare(remote1, share12, drive.PermissionReadOnly)
 	s.writeFile("writing file to read-only remote should fail", remote1, share12, file111, "hello world", false)
-
 	s.writeFile("writing file to non-existent remote should fail", "non-existent", share11, file111, "hello world", false)
 	s.writeFile("writing file to non-existent share should fail", remote1, "non-existent", file111, "hello world", false)
 }
@@ -241,7 +246,18 @@ func (s *system) writeFile(label, remoteName, shareName, name, contents string,
 	if expectSuccess && err != nil {
 		s.t.Fatalf("%v: expected success writing file %q, but got error %v", label, path, err)
 	} else if !expectSuccess && err == nil {
-		s.t.Fatalf("%v: expected error writing file %q", label, path)
+		s.t.Fatalf("%v: expected error writing file %q, but got no error", label, path)
+	}
+}
+
+func (s *system) renameFile(label, remoteName, fromShare, fromFile, toShare, toFile string, expectSuccess bool) {
+	fromPath := pathTo(remoteName, fromShare, fromFile)
+	toPath := pathTo(remoteName, toShare, toFile)
+	err := s.client.Rename(fromPath, toPath, true)
+	if expectSuccess && err != nil {
+		s.t.Fatalf("%v: expected success moving file %q to %q, but got error %v", label, fromPath, toPath, err)
+	} else if !expectSuccess && err == nil {
+		s.t.Fatalf("%v: expected error moving file %q to %q, but got no error", label, fromPath, toPath)
 	}
 }
 
diff --git a/drive/driveimpl/shared/pathutil.go b/drive/driveimpl/shared/pathutil.go
index 49f8ba849..748f75701 100644
--- a/drive/driveimpl/shared/pathutil.go
+++ b/drive/driveimpl/shared/pathutil.go
@@ -4,6 +4,7 @@
 package shared
 
 import (
+	"net/url"
 	"path"
 	"strings"
 )
@@ -35,6 +36,16 @@ func Join(parts ...string) string {
 	return path.Join(fullParts...)
 }
 
+// JoinEscaped is like Join but path escapes each part.
+func JoinEscaped(parts ...string) string {
+	fullParts := make([]string, 0, len(parts))
+	fullParts = append(fullParts, sepString)
+	for _, part := range parts {
+		fullParts = append(fullParts, url.PathEscape(part))
+	}
+	return path.Join(fullParts...)
+}
+
 // IsRoot determines whether a given path p is the root path, defined as either
 // empty or "/".
 func IsRoot(p string) bool {