The phenomenon of anchoring seems to predict that deadlines will cause you to start a project near the deadline.
In more detail:
Any number you consider as an answer to a question will become an anchor and draw your answer towards it. Since you consider a deadline as a time to finish a project, your decision about when you should actually finish the project will be drawn towards it.
That'll make you start the project later, even though you know consciously that planning to finish a project near the deadline is a bad idea.
It's analogous to an example from Kahneman's Thinking, Fast and Slow—people buy more cans when there's a sign telling them that they can only buy 10.
So, what I'm predicting is that anything that prevents anchoring will reduce procrastination when there's a deadline. Consciously deciding when you plan to finish by adjusting from a much earlier time, maybe?
EDIT: Brendon_Wong points out that "procrastination" really refers to putting things off, which has an emotional cause. I think he's right. What I'm talking about isn't really a procrastination, then, but bad planning.
It is a bad thing, because you should do something at the best time, not when it's urgent. They won't usually happen to coincide.
For example, the best time to write essays for med school applications is over the summer, because you have free time; not near the deadlines which are around December, when you'll be taking classes.
I think it's missing the point to claim that the deadlines are causing you to procrastinate in this case. If there weren't any deadlines for med school applications, what would it even mean to procrastinate on them?
It's also not clear to me that the best time to work on med school applications is in fact over the summer. There are other things you could be doing with that luxuriously free summer time. During the school year you're working on various unpleasant things already, so you might as well lump one more unpleasant thing in there. (I did my grad school applications in November of the relevant year and that was fine.)