Yup, there is a special trick. It's called sending out as many requests as possible and wait for them to be filled. You can limit the number of downloads that occur at the same time, if you're worried about bandwidth ... In general, the larger the file you want, and the more popular it is, the longer you'll have to wait for the requests to actually find an open download slot. Simply send requests to all the hosts that have the file, and update your search results often.

The other special trick is to continue to share your files, and encourage others to do the same. The greater the number of shared files on the network, the better chance there is that requests will be filled quickly.