I want a search box on my site that injects the "site:http://mysite.com" alongside the user's query term. They type in "foo", the search ends up being "site:mysite.com foo".

This worked fine with Google using a hidden input in the form. It would run a search like https://encrypted.google.com/search?q=site&q=foo, so the search query ended up as "site foo".

I don't want to use Google: I want to use DDG. But when I run the corresponding DDG search https://duckduckgo.com/?q=site&q=foo, the search text ends up being just "foo". Last q= wins, I guess.

Any workarounds or other suggestions?

ETA: The interface I'm talking about is the Search box to the top right of http://octopress.org/. You type in a term, it searches just that site for the term.