Just a small proportion of parents of children heading to college are putting money aside in state 529 savings plans, though a new analysis finds that many of the plans have been making themselves more attractive by reducing fees.

In its annual rating of the plans, the investment research company Morningstar noted that the industry had been making significant fee cuts, so plans become less competitive if they don’t follow suit.

The company analyzed 62 plans, comprising the bulk of money held in 529 accounts, and rated 31 as the best based on factors like fees, choice of investments and strong professional oversight.

The accounts, which are authorized by Section 529 of the Internal Revenue Code, are offered through state-sponsored programs to help people invest for higher education. Money withdrawn from 529 plans is tax free as long as it is spent on tuition, fees and other eligible costs, like room and board, books and equipment.