A troubling number of high school students only applied to one college last year. (Photo by Mary F. Calvert for The Washington Post)

You know the old adage don’t put all your eggs in one basket? Despite that conventional wisdom, a troubling number of high school students only applied to only one college last year.

Nearly two-thirds of students filling out the 2014-15 FAFSA, which the government and colleges use to determine need- and some merit-based financial aid, listed one college on the form, according to data released Thursday by the Department of Education. While that’s better than the 80 percent who recorded one school in 2008-2009, too many students are selling themselves short.

Here are a few reasons why:

Hedging Your Bets: News flash, the more places you apply, the better your chances of getting accepted somewhere. No one is saying high school seniors should send off 10 or 20 applications; not only is that time consuming, but it could also burn a hole in your wallet. Yet guidance counselors say that having at least one “reach” and one “safe” school is a good strategy.

[When it does matter where you go to college]

Better Financial Aid Awards: Your child may have her heart set on the local flagship university, but it’s entirely possible that another school of equal or greater stature will be cheaper. This is especially true for smart, low-income students who could get into an elite school with the money to cover the cost of their education. Research has shown those students have a higher chance of graduating from highly-selective colleges, something to consider.

On the flip side, your child certainly doesn’t have to attend a brand-name school to get a stellar education. Pay attention to the quality of the program. The school may not be top tier overall, but its engineering program might be.

[How to negotiate a better financial aid package]

Financial Leverage: While this is far from a sure fire bet, some schools are willing to adjust their award of scholarships and grants to match a better offer from another college. The thing is, the schools would have to be at least equally ranked and your kid would have to be a pretty good student. Don’t expect a bidding war, but if a college wants your child, the financial aid administrators may be willing to budge on the aid package.

Want to read more about paying for college? Check out these stories:

How your family finances factor into financial aid calculators

What to do when you haven’t saved much for your kid’s college education

Middle-class families are fed up with their financial aid options