There are other ways to communicate priorities. For example:

"What were you planning to work on in the next few days? ... This is more important than any of those things. I'd like you to work on this first, please, and get it back to me as soon as possible."

"See if you can fit this into your schedule, although it's lower priority than projects A and B."

"How much actual work time do you think it would take you to do this? ... Never mind: I'll get someone else to do it. I need you to focus your energy on A and B."

"As soon as you've finished A, I'd like you to work on this and get the results to me
before you start on B."

"This is important. I suggest you spend at least 50% of your time on it until it's
completed."

Also, as mcogilvie suggested, it's good to give the actual reason why you need it soon.
"As soon as we have this from you, these three other people and I will be able to
start on this project we've been eager to get going on ..."

Also, after you actually receive the results, thank the person, publicly give them
credit and give them some information about how you've used it.
"Thanks. This is just what I wanted. Now I can start on ..."
"By the way, that stuff you gave me last week was really useful because ..."
"This has been a team effort; I'd like to thank the following people who
contributed ..." Then they may be more willing to do stuff for you the
next time.