You have to specialize. If you can do that, you will be the first choice of those interested in your area of specialization, so the best ones will come.
Today's globalization has created "winner takes it all" markets, and the education market is not so different. In this style of market, the top players get many times more customers than second-tier players, second-tier players do much better than third-tier players, and so on. The differences between the tiers are huge, and each place in the first few tiers of the global market is already occupied. The competition is ferocious.
So currently, you are getting two types of student: A) Those for whom you are accidentally special, e.g. they live in your city and don't want to move, and B) those who dreamed to get into Harvard. A will contain the usual mix of brilliant and average students, while from B, Harvard picked all the chocolate chips from the cookie.
The solution is that you become top player by getting into a niche which has been overlooked. It may be completely new, or it may have 1-2 players which are in it accidentally, so you can beat them easily. Suddenly, you'll start getting applications from C), the students who dream of being in that niche. Not only did you open yourself to a new set of students, but those who know early on what they know, and find out which university offers it, tend to be the best. This is a set of self-selected people who are motivated and effective.
The good thing is that, once your core excellence area builds you a reputation, it rubs off on the whole department. If you are a computer science department and become the place to study formal verification methods, many future students will not hear specifically about the formal verification methods, or know what they are. They will have simply heard that there are good people vying for admission at your department, and conclude that they want to go there too.
You asked for short-term tactics, and I'm talking about reputation. But you can certainly start now short-term. The thing to do is to pick your niche right now, and recast your PR material to support it. Maybe even try to make some lightweight changes to teaching to support the new orientation, such as changing the names of existing courses to better show how they are connected to the niche you are going to claim.
By the way, the currently most upvoted answer - attract minorities - is also going in this direction. It suggests that you occupy a social niche, instead of a discipline-based niche. The good thing is that you don't have to choose, you can do both in parallel.
I realize that any good intentions in this direction are likely to get mired in politics and stopped at many levels, so this won't succeed in many cases, unless championed by somebody with sufficient power. This doesn't mean that the answer is wrong, just that it is difficult to do it right.