Custom Drupal 6 Module with multiple pages - drupal

Question

I am trying to write my first Drupal custom module (using drupal 6). I got the basic module working but I would like to add another page to the project. For example, right now my module's path looks like this: www.mysite.com/my_custom_module. I would like to add another page like this: www.mysite.com/my_custom_module/my_sub_page. I've tried adding a new .module and .info file but this does not work. I've also tried adding new items to the menu hook, like this:
my_custom_module.module:
function my_custom_module_menu(){
$items = array();
$items['my_custom_module'] = array(
'title' => "My Custom Module",
'page callback' => "my_custom_module_info",
'access callback' => true,
'type' => MENU_NORMAL_ITEM,
);
$items['my_custom_module/my_sub_page'] = array(
'title' => "My Sub Page",
'page callback' => "my_custom_module_sub_page_info",
'access callback' => true,
'type' => MENU_NORMAL_ITEM,
);
return $items;
}
function my_custom_module_info(){
$result = 'My Page URL was hit';
return $result;
}
function my_custom_module_sub_page_info(){
$result = 'My Sub Page URL was hit';
return $result;
}
In this example, if I go to .../my_custom_module it works fine. But, if I go to .../my_custom_module/my_sub_page, it still load, and displays my_custom_module. When I debug with a break point in each function, only my_custom_module_info is hit. Not the sub page. What am I doing wrong? I this even the correct way to create multi pages in a module? Just an FYI, each of these pages will have different audiences. The first page is to allow a user to submit some form data. The second is to allow an elevated user view the data.
Thanks
jason