Nice Menus drop down bug

A good, simple module for Drupal called Nice Menus has an annoying bug (supposedly not on all themes, but certainly on most of them): It frequently loses the focus when the mouse moves from the top-level menu to a child menu, causing the drop-down menu to disappear as the user goes to click on it.

Very annoying. (If you click and hold and move the mouse down, the second-level menu stays and you can then click on it. Not exactly a solution you can ask your users to do.)

The fix can vary depending on the site. For instance, the first fix listed below worked on Agaric Design's site here, but all the way to the third fix was needed for a client. In any case, the surest fixes seem to be moving pixels around until there's a consistent overlap (visually indistinguishable from normal behavior).