diff --git a/src/combiner.rs b/src/combiner.rs
index d084a85..3b827a3 100644
--- a/src/combiner.rs
+++ b/src/combiner.rs
@@ -83,15 +83,18 @@ impl Combiner {
                 bail!("incorrect installer version in {}", input_tarball);
             }
 
-            // Move components to the new combined installer
+            // Copy components to the new combined installer
             let mut pkg_components = String::new();
             open_file(pkg_dir.join("components"))
                 .and_then(|mut file| file.read_to_string(&mut pkg_components).map_err(Error::from))
                 .chain_err(|| format!("failed to read components in '{}'", input_tarball))?;
             for component in pkg_components.split_whitespace() {
-                // All we need to do is move the component directory
+                // All we need to do is copy the component directory.  We could
+                // move it, but rustbuild wants to reuse the unpacked package
+                // dir for OS-specific installers on macOS and Windows.
                 let component_dir = package_dir.join(&component);
-                rename(&pkg_dir.join(&component), component_dir)?;
+                create_dir(&component_dir)?;
+                copy_recursive(&pkg_dir.join(&component), &component_dir)?;
 
                 // Merge the component name
                 writeln!(&components, "{}", component)
diff --git a/src/util.rs b/src/util.rs
index acc269a..d5beed1 100644
--- a/src/util.rs
+++ b/src/util.rs
@@ -79,13 +79,6 @@ pub fn remove_file<P: AsRef<Path>>(path: P) -> Result<()> {
         .chain_err(|| format!("failed to remove file '{}'", path.as_ref().display()))
 }
 
-/// Wrap `fs::rename` with a nicer error message
-pub fn rename<P: AsRef<Path>, Q: AsRef<Path>>(from: P, to: Q) -> Result<()> {
-    fs::rename(&from, &to)
-        .chain_err(|| format!("failed to rename '{}' to '{}'",
-                              from.as_ref().display(), to.as_ref().display()))
-}
-
 /// Copies the `src` directory recursively to `dst`. Both are assumed to exist
 /// when this function is called.
 pub fn copy_recursive(src: &Path, dst: &Path) -> Result<()> {
diff --git a/test.sh b/test.sh
index 1012dd8..c85e4d3 100755
--- a/test.sh
+++ b/test.sh
@@ -946,6 +946,38 @@ list_components() {
 }
 runtest list_components
 
+combined_remains() {
+    try sh "$S/gen-installer.sh" \
+	--image-dir="$TEST_DIR/image1" \
+	--work-dir="$WORK_DIR" \
+	--output-dir="$OUT_DIR" \
+	--package-name=rustc \
+	--component-name=rustc
+    try sh "$S/gen-installer.sh" \
+	--image-dir="$TEST_DIR/image3" \
+	--work-dir="$WORK_DIR" \
+	--output-dir="$OUT_DIR" \
+	--package-name=cargo \
+	--component-name=cargo
+    try sh "$S/gen-installer.sh" \
+	--image-dir="$TEST_DIR/image4" \
+	--work-dir="$WORK_DIR" \
+	--output-dir="$OUT_DIR" \
+	--package-name=rust-docs \
+	--component-name=rust-docs
+    try sh "$S/combine-installers.sh" \
+	--work-dir="$WORK_DIR" \
+	--output-dir="$OUT_DIR" \
+	--package-name=rust \
+	--input-tarballs="$OUT_DIR/rustc.tar.gz,$OUT_DIR/cargo.tar.gz,$OUT_DIR/rust-docs.tar.gz"
+    for component in rustc cargo rust-docs; do
+	# rustbuild wants the original extracted package intact too
+	try test -d "$WORK_DIR/$component/$component"
+	try test -d "$WORK_DIR/rust/$component"
+    done
+}
+runtest combined_remains
+
 # Upgrade tests
 
 upgrade_from_v1() {