You can use WordPress’ ability to accept custom rewrite rules to get this done. You can add the following to your functions file, or create a plugin (recommended).
function url_rewrites_wpanswers() {
add_rewrite_rule('/custom-post-type-slug/([^/]*)?$','index.php?post_type=custom-post-type-name&custom-taxonomy-name=$matches[1]', 'top'); //lets you use /posttype/customtaxterm
}
add_action('init','url_rewrites_wpanswers');
You would have to add a line for each since otherwise yoursite.com/something1/something2 would end up pointing to:
yoursite.com/index.php?post_type=something1&custom-taxonomy-name=something2
Keep in mind, with the functionality that you are requesting there can be conflicts with your permalinks if they are set to /post-type/post-name
You can read and learn more here: http://codex.wordpress.org/Rewrite_API/add_rewrite_rule