diff --git a/client.go b/client.go
index 8802ed7..13209d0 100644
--- a/client.go
+++ b/client.go
@@ -247,16 +247,28 @@ func (c *Client) Mkdir(ctx context.Context, name string) error {
 	return nil
 }
 
-// CopyAll copies a file. If the file is a directory, all of its descendants
-// are recursively copied as well.
-func (c *Client) CopyAll(ctx context.Context, name, dest string, overwrite bool) error {
+// Copy copies a file.
+//
+// By default, if the file is a directory, all descendants are recursively
+// copied as well.
+func (c *Client) Copy(ctx context.Context, name, dest string, options *CopyOptions) error {
+	if options == nil {
+		options = new(CopyOptions)
+	}
+
 	req, err := c.ic.NewRequest("COPY", name, nil)
 	if err != nil {
 		return err
 	}
 
+	depth := internal.DepthInfinity
+	if options.NoRecursive {
+		depth = internal.DepthZero
+	}
+
 	req.Header.Set("Destination", c.ic.ResolveHref(dest).String())
-	req.Header.Set("Overwrite", internal.FormatOverwrite(overwrite))
+	req.Header.Set("Overwrite", internal.FormatOverwrite(!options.NoOverwrite))
+	req.Header.Set("Depth", depth.String())
 
 	resp, err := c.ic.Do(req.WithContext(ctx))
 	if err != nil {
diff --git a/fs_local.go b/fs_local.go
index 1366f4b..84d38b1 100644
--- a/fs_local.go
+++ b/fs_local.go
@@ -154,7 +154,7 @@ func copyRegularFile(src, dst string, perm os.FileMode) error {
 	return dstFile.Close()
 }
 
-func (fs LocalFileSystem) Copy(ctx context.Context, src, dst string, recursive, overwrite bool) (created bool, err error) {
+func (fs LocalFileSystem) Copy(ctx context.Context, src, dst string, options *CopyOptions) (created bool, err error) {
 	srcPath, err := fs.localPath(src)
 	if err != nil {
 		return false, err
@@ -179,7 +179,7 @@ func (fs LocalFileSystem) Copy(ctx context.Context, src, dst string, recursive,
 		}
 		created = true
 	} else {
-		if !overwrite {
+		if options.NoOverwrite {
 			return false, os.ErrExist
 		}
 		if err := os.RemoveAll(dstPath); err != nil {
@@ -202,7 +202,7 @@ func (fs LocalFileSystem) Copy(ctx context.Context, src, dst string, recursive,
 			}
 		}
 
-		if fi.IsDir() && !recursive {
+		if fi.IsDir() && options.NoRecursive {
 			return filepath.SkipDir
 		}
 		return nil
diff --git a/server.go b/server.go
index 617cb69..b7eb225 100644
--- a/server.go
+++ b/server.go
@@ -20,7 +20,7 @@ type FileSystem interface {
 	Create(ctx context.Context, name string) (io.WriteCloser, error)
 	RemoveAll(ctx context.Context, name string) error
 	Mkdir(ctx context.Context, name string) error
-	Copy(ctx context.Context, name, dest string, recursive, overwrite bool) (created bool, err error)
+	Copy(ctx context.Context, name, dest string, options *CopyOptions) (created bool, err error)
 	MoveAll(ctx context.Context, name, dest string, overwrite bool) (created bool, err error)
 }
 
@@ -231,7 +231,11 @@ func (b *backend) Mkcol(r *http.Request) error {
 }
 
 func (b *backend) Copy(r *http.Request, dest *internal.Href, recursive, overwrite bool) (created bool, err error) {
-	created, err = b.FileSystem.Copy(r.Context(), r.URL.Path, dest.Path, recursive, overwrite)
+	options := CopyOptions{
+		NoRecursive: !recursive,
+		NoOverwrite: !overwrite,
+	}
+	created, err = b.FileSystem.Copy(r.Context(), r.URL.Path, dest.Path, &options)
 	if os.IsExist(err) {
 		return false, &internal.HTTPError{http.StatusPreconditionFailed, err}
 	}
diff --git a/webdav.go b/webdav.go
index 7397f9f..73a9c7f 100644
--- a/webdav.go
+++ b/webdav.go
@@ -16,3 +16,8 @@ type FileInfo struct {
 	MIMEType string
 	ETag     string
 }
+
+type CopyOptions struct {
+	NoRecursive bool
+	NoOverwrite bool
+}