Possible to limit the height of auto-suggest?

I’m curious if it is possible to require a certain number of characters before populating the auto-suggest – or limit the length of the number of auto-suggestions options which are displayed?

Currently the drop-down list extends too far and overlaps the Google ads on the site which is a violation of Google’s policies because it promotes accidental clicks in their eyes.

I’d love to limit the number of auto-suggested items – and also require a certain number of characters to be entered before the auto suggest activates. There’s no reason to start it with just one character entered.