diff --git a/cache.h b/cache.h
index 04951ddcbf..4d02efc905 100644
--- a/cache.h
+++ b/cache.h
@@ -1254,6 +1254,10 @@ extern int unpack_object_header(struct packed_git *, struct pack_window **, off_
  *
  * Any callback that is NULL will be ignored. Callbacks returning non-zero
  * will end the iteration.
+ *
+ * In the "buf" variant, "path" is a strbuf which will also be used as a
+ * scratch buffer, but restored to its original contents before
+ * the function returns.
  */
 typedef int each_loose_object_fn(const unsigned char *sha1,
 				 const char *path,
@@ -1269,6 +1273,11 @@ int for_each_loose_file_in_objdir(const char *path,
 				  each_loose_cruft_fn cruft_cb,
 				  each_loose_subdir_fn subdir_cb,
 				  void *data);
+int for_each_loose_file_in_objdir_buf(struct strbuf *path,
+				      each_loose_object_fn obj_cb,
+				      each_loose_cruft_fn cruft_cb,
+				      each_loose_subdir_fn subdir_cb,
+				      void *data);
 
 /*
  * Iterate over loose and packed objects in both the local
diff --git a/sha1_file.c b/sha1_file.c
index 30995e61b3..69a60ec88b 100644
--- a/sha1_file.c
+++ b/sha1_file.c
@@ -3359,31 +3359,42 @@ static int for_each_file_in_obj_subdir(int subdir_nr,
 	return r;
 }
 
-int for_each_loose_file_in_objdir(const char *path,
+int for_each_loose_file_in_objdir_buf(struct strbuf *path,
 			    each_loose_object_fn obj_cb,
 			    each_loose_cruft_fn cruft_cb,
 			    each_loose_subdir_fn subdir_cb,
 			    void *data)
 {
-	struct strbuf buf = STRBUF_INIT;
-	size_t baselen;
+	size_t baselen = path->len;
 	int r = 0;
 	int i;
 
-	strbuf_addstr(&buf, path);
-	strbuf_addch(&buf, '/');
-	baselen = buf.len;
-
 	for (i = 0; i < 256; i++) {
-		strbuf_addf(&buf, "%02x", i);
-		r = for_each_file_in_obj_subdir(i, &buf, obj_cb, cruft_cb,
+		strbuf_addf(path, "/%02x", i);
+		r = for_each_file_in_obj_subdir(i, path, obj_cb, cruft_cb,
 						subdir_cb, data);
-		strbuf_setlen(&buf, baselen);
+		strbuf_setlen(path, baselen);
 		if (r)
 			break;
 	}
 
+	return r;
+}
+
+int for_each_loose_file_in_objdir(const char *path,
+				  each_loose_object_fn obj_cb,
+				  each_loose_cruft_fn cruft_cb,
+				  each_loose_subdir_fn subdir_cb,
+				  void *data)
+{
+	struct strbuf buf = STRBUF_INIT;
+	int r;
+
+	strbuf_addstr(&buf, path);
+	r = for_each_loose_file_in_objdir_buf(&buf, obj_cb, cruft_cb,
+					      subdir_cb, data);
 	strbuf_release(&buf);
+
 	return r;
 }
 
@@ -3396,9 +3407,16 @@ static int loose_from_alt_odb(struct alternate_object_database *alt,
 			      void *vdata)
 {
 	struct loose_alt_odb_data *data = vdata;
-	return for_each_loose_file_in_objdir(alt->base,
-					     data->cb, NULL, NULL,
-					     data->data);
+	struct strbuf buf = STRBUF_INIT;
+	int r;
+
+	/* copy base not including trailing '/' */
+	strbuf_add(&buf, alt->base, alt->name - alt->base - 1);
+	r = for_each_loose_file_in_objdir_buf(&buf,
+					      data->cb, NULL, NULL,
+					      data->data);
+	strbuf_release(&buf);
+	return r;
 }
 
 int for_each_loose_object(each_loose_object_fn cb, void *data)
diff --git a/t/t5304-prune.sh b/t/t5304-prune.sh
index e32e46dee1..0794d33dad 100755
--- a/t/t5304-prune.sh
+++ b/t/t5304-prune.sh
@@ -253,4 +253,12 @@ test_expect_success 'prune .git/shallow' '
 	test_path_is_missing .git/shallow
 '
 
+test_expect_success 'prune: handle alternate object database' '
+	test_create_repo A &&
+	git -C A commit --allow-empty -m "initial commit" &&
+	git clone --shared A B &&
+	git -C B commit --allow-empty -m "next commit" &&
+	git -C B prune
+'
+
 test_done