Limiting the menu levels for "Custom menu" widget

I would like to have two menus, one for level 1 elements on the top and an other one with the current branch on the left side for level 2, 3, 4.

Now I am using a simple “Custom menu” widget for the second menu, but I cannot limit it to show only levels 2, 3, 4. Is there any modification for the custom menu or a plugin for an “Advanced Custom Menu” widget?

One possible way I think about is to set a css rule for something like this:

#secondary li {display: none;}
#secondary li.current-menu-ancestor {display: inherit;}

Isn’t there a more elegant solution than a CSS hack?