diff --git a/internal/codespaces/ssh.go b/internal/codespaces/ssh.go
index b54dff0dc..1807c87fa 100644
--- a/internal/codespaces/ssh.go
+++ b/internal/codespaces/ssh.go
@@ -27,16 +27,23 @@ func Shell(ctx context.Context, log logger, sshArgs []string, port int, destinat
 
 // Copy runs an scp command over the specified port. The arguments may
 // include flags and non-flags, optionally separated by "--".
-// Remote files are indicated by a "user@host:" prefix.
-func Copy(ctx context.Context, scpArgs []string, port int) error {
+// Remote files are indicated by a "remote:" prefix, and are resolved
+// relative to the remote user's home directory.
+func Copy(ctx context.Context, scpArgs []string, port int, destination string) error {
 	// Beware: invalid syntax causes scp to exit 1 with
 	// no error message, so don't let that happen.
-	scpArgs = append([]string{
+	cmd := exec.CommandContext(ctx, "scp",
 		"-P", strconv.Itoa(port),
 		"-o", "NoHostAuthenticationForLocalhost=yes",
 		"-C", // compression
-	}, scpArgs...)
-	cmd := exec.CommandContext(ctx, "scp", scpArgs...)
+	)
+	for _, arg := range scpArgs {
+		// Replace "remote:" prefix with (e.g.) "root@localhost:".
+		if rest := strings.TrimPrefix(arg, "remote:"); rest != arg {
+			arg = destination + ":" + rest
+		}
+		cmd.Args = append(cmd.Args, arg)
+	}
 	cmd.Stdin = nil
 	cmd.Stdout = os.Stderr
 	cmd.Stderr = os.Stderr
diff --git a/pkg/cmd/codespace/ssh.go b/pkg/cmd/codespace/ssh.go
index 91b8a2e7e..d0d3e49fe 100644
--- a/pkg/cmd/codespace/ssh.go
+++ b/pkg/cmd/codespace/ssh.go
@@ -124,7 +124,7 @@ func (a *App) SSH(ctx context.Context, sshArgs []string, opts sshOptions) (err e
 	go func() {
 		var err error
 		if opts.scpArgs != nil {
-			err = codespaces.Copy(ctx, opts.scpArgs, localSSHServerPort)
+			err = codespaces.Copy(ctx, opts.scpArgs, localSSHServerPort, connectDestination)
 		} else {
 			err = codespaces.Shell(ctx, a.logger, sshArgs, localSSHServerPort, connectDestination, usingCustomPort)
 		}
@@ -157,7 +157,8 @@ func newCpCmd(app *App) *cobra.Command {
 The cp command copies files between the local and remote file systems.
 
 A 'remote:' prefix on any file name argument indicates that it refers to
-the file system of the remote (Codespace) machine.
+the file system of the remote (Codespace) machine. It is resolved relative
+to the home directory of the remote user.
 
 As with the UNIX cp command, the first argument specifies the source and the last
 specifies the destination; additional sources may be specified after the first,
@@ -187,11 +188,7 @@ func (a *App) Copy(ctx context.Context, args []string, opts cpOptions) (err erro
 	}
 	opts.scpArgs = append(opts.scpArgs, "--")
 	for _, arg := range args {
-		if rest := strings.TrimPrefix(arg, "remote:"); rest != arg {
-			// TODO(adonovan): don't assume user=root:
-			// use value from session.StartSSHServer.
-			arg = "root@localhost:" + rest
-		} else if !filepath.IsAbs(arg) {
+		if !filepath.IsAbs(arg) && !strings.HasPrefix(arg, "remote:") {
 			// scp treats a colon in the first path segment as a host identifier.
 			// Escape it by prepending "./".
 			// TODO(adonovan): test on Windows, including with a c:\\foo path.