Fact: Americans stink at saving. That’s bad news since pensions are increasingly a rarity these days, leaving people on their own when it comes to tucking away money for the future. But a recent study suggests that people are somewhat self-aware about what crummy savers they are, and if given the chance, they’ll choose accounts that impose self control.

The paper, authored by John Beshears, David Laibson, and Brigitte C. Madrian of Harvard; James J. Choi of Yale; Christopher Harris of Cambridge; and Jung Sakong of University of Chicago, looked at the savings habits of 1,045 adults who were offered accounts with varying levels of restrictiveness in order to see how higher penalties on withdrawals affected savings behavior. All participants could access a regular, highly liquid bank account (like a checking account). They were then also given access to accounts that either put penalties on withdrawals or prohibited them all together.

The result: When confronted with the choice between stashing their money in an account where they could easily access it, or putting it into an account that would restrict their ability to use their cash, participants consistently stowed about half of their money in a savings account. Even when the more restrictive account had a lower interest rate than their normal account, participants still funneled about 25 percent of their money into it.

In fact, participants actually favored the most restrictive accounts when all accounts offered the same interest rate. In that scenario, those who were given an account that imposed a 10 percent penalty deposited less into their savings account than those whose accounts faced a 20 percent withdrawal penalty. And those whose accounts didn’t allow any withdrawals at all stashed the highest share of their money in savings—about two times as much as those who would only face a 10 percent fee. Researchers say that these results may suggest that participants were aware of their lack of self-control, and took advantage of mechanisms that would prevent them from sabotaging their savings.

But when the interest rate on the savings account was higher than on the regular account (like it is for most 401(k)s and IRAS), participants still socked away money in savings, but they chose the least restrictive savings account about as much as they chose the account that wouldn’t allow any withdrawals. That may mean that a better interest rate actually discouraged participants from being more disciplined with their savings, since they felt like their savings account would grow more quickly, making early withdrawals less problematic.

The findings are especially pertinent now that 401(k) and IRA plans have grown to dominate the American retirement-savings landscape. These types of savings accounts are only somewhat illiquid—meaning that account holders typically face a penalty of about 10 percent if they choose to take money out before they reach a certain age, but they still have access to their funds. In many other countries, drawing down on retirement savings is much more difficult, if not impossible.

In theory having access to hard-saved cash might feel like a smart safety net, but taking it out now means that families lose out in the long run—especially since they’ll miss the compounding interest that accrues in long-term savings accounts. Capitalism may be helpful when it comes to providing people with choices, but saving for retirement is a case where fewer options may be what people actually want.