Any way to keep search values after submit?

I just discovered Custom Search, and it has solved many concerns I had for searches on a big site I'm creating.

But one issue I can't figure out is whether there is a setting to retain the user's search values on the search results page. To me, it seems logical to want to tailor a search after seeing the results, and having all the form fields be set would make that much easier for the user.

(I see these values in the URL arguments, but my users will not be sophisticated enough to modify those by hand.)

Thanks for any advice!