We sell our product hosted, and on a regular basis we get sales knocking on our door: a customer wants this-and-that report (followed by a 20-word description), how long will that take us, they need it fast?
In the past we tried to get more information, it never came, sales looked at us like: "this description looks pretty clear to me, what else do you need to know", we still estimated, and we ended up losing money, and/or the project went completely sideways.
Usually these things should take a few weeks at most, so they are small, but as a company we really can use the cash.
I always ask the programmer that is intended to do the actual work, but they come back with either no estimate, or with a far too high cover-my-ass estimate, which we cannot sell.
What's the best way to handle this?
Also, you should consider adding a rush fee, partially just to give yourself some buffer. (But also to separate the folks who actually need it fast from the ones who are just jerks.)
Oh, and one last note: the customers that pay more tend to be more pleasant to work with. So those "far too high cover-my-ass estimates" might not be such a bad idea sometimes ;)