It depends, for example, on what tax rate you’re paying now, compared to what tax bracket you’ll be in when you retire. Traditional 401(k)s, along with traditional individual retirement accounts, lower your taxes now, but you end paying at the other end, when you take the money out in retirement. With a Roth account, you pay taxes now, but all withdrawals later, including investment gains, are tax-free.

It’s pretty clear, then, that Roth accounts should work well for young, low-paid workers, who are probably paying the lowest tax rates of their careers. And a recent study suggested that workers may end up unintentionally contributing more to Roth 401(k) accounts than to traditional 401(k)s, albeit unintentionally.

The benefits of a Roth are less obvious for older or wealthier workers, who are paying high tax rates now and don’t know what their taxes will look like in 20 or 30 years. How do they balance lowering their tax rate now, using a traditional account, with the advantages of a Roth’s tax-free pool of money in retirement?

Cederburg decided to find out. A new study, which he conducted with two other finance professors—David C. Brown of the University of Arizona and Michael O’Doherty of the University of Missouri—used software to simulate the optimal saving strategies for a million retirement scenarios over the next 30 years.

Their conclusion: Most investors, including wealthy ones, end up better off with a mix of assets in traditional and Roth accounts.

Each kind of account has advantages, the study found. Traditional 401(k)s and IRAs can be used strategically to lower your current tax rate, which is especially valuable when a traditional contribution bumps you down to a lower tax bracket. Roth accounts insure against the chance that tax rates will spike as baby boomers retire, health-care costs rise, or the nation faces a more serious fiscal crisis.

“It’s tough to say what the world will look like in 30 years,” Cederburg said. “With a Roth account, you can lock in current tax rates.”

The study modeled the future based on past investment returns and tax rates, which were anything but stable. Since 1913, the marginal tax rate has changed 39 times for a single person with an inflation-adjusted income of $100,000, varying from 1 percent to 43 percent. The wealthiest Americans have paid an even wider range of rates. For 15 years in the mid-20th century, the top tax bracket was above 90 percent.

While well-paid workers are often told to skip Roth 401(k)s entirely, the new paper could change that advice. "This suggests that Roth accounts should be given a more serious look by those in high tax brackets,” said Daniel Ostrov, a Santa Clara University math professor who has written about (PDF) Roth and traditional retirement strategies and who praised the Cederburg study as “quite good.”

Though the study tried to quantify optimal strategies, finding significant benefits in mixing Roth and traditional accounts for almost all savers, its simplified model doesn't offer a recipe. Cederburg and his colleagues couldn’t take into account certain distinct advantages of each option. Assets in a Roth are easier to withdraw before retirement and don’t require mandatory withdrawals when you get older. Traditional accounts can sometimes be converted to Roth IRAs in a way that avoids taxes. And there's always the small chance that Congress could change the rules for Roth accounts and make them less valuable.

For his part, Cederburg, 34 years old and saving for a retirement that won’t start until 2050, decided to split his contributions 50/50 between Roth and traditional options. Many employees don’t have the option. A Vanguard Group study last month of its own 401(k) plans found that 40 percent of employers don’t offer Roth accounts.

“What is clear from the paper," Ostrov said, "is that every company should give their employees a Roth option to save for retirement.”

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