I don't mean a complete repost, but rewriting the question to be more interesting, more general, so that more people read it, and possibly write an answer.
If you're just adding some details that you originally left out, or clarifying part of your original question that you later realized was misleading, then edit your question. It'll get bumped, and maybe gain enough attention to help you find an answer.
If you realize that your original question was misguided, and you really should have asked something else (perhaps you realized this as a result of an answer or comment on your first question...), then post a new one. You can link to the first question to provide some background, but don't skimp on details - the new question should stand on its own.
If you have nothing to add or change, but just aren't happy with the amount of attention your question received, then consider adding a bounty to it. You may be asking something that requires a significant amount of research on a niche topic, and would benefit from "sweetening the deal" a bit...
It would be best to rewrite the answer as an edit to your original question. Though you may not get to the top of the new questions list, you will get the same exposure at the top of the home view.
Also, if you really want to get better answers than those that your original wording provoked use the bounty feature to entice feedback.