One reason we don’t see nearly enough wage growth in the US labor market is that employers rarely have to compete for workers. Often this is due to weak demand (persistent labor market slack), but discrimination by race and gender and low unionization rates can also play a role in reduced worker bargaining power.

A new report from the White House suggests another, quite direct form of this problem: “non-compete agreements” (NCAs), “contracts that ban workers at a certain company from going to work for a competing employer within a certain period of time after leaving a job.”

The rationale for such agreements is the protection of “trade secrets.” Without them, companies argue, employees could learn proprietary information and then market it to rival companies in return for a better employment offer. Relatedly, companies worry that they will invest time and money into employee training only to miss out on the rewards of that investment (while their competitors gain) when freshly trained employees jump ship.

Such concerns have merit, but surely not for every type of worker. The report tells, for example, of a national sandwich chain that “required its employees to sign an expansive non-compete agreement that would ban them from working at just about any other fast-food restaurant.” Yes, some of these shops tout their “secret sauce,” but this practice reeks of suppressed competition and pay.

In fact, the White House finds that 15 percent of non-college graduates are subject to NCAs, as are 14 percent of workers earning less than $40,000 (according to my analysis, 14 percent of jobs under that pay level amounts to about 12 million workers). Add that information to the fact that most workers with NCAs claim not to possess trade secrets and one gets a sense of the problem.

Unnecessary bans on labor mobility are bad for workers and bad for the broader economy, as efficient matching between workers and jobs requires freedom of movement. But is there any evidence that NCAs actually dampen worker bargaining power/negotiating leverage? In fact, the research finds that a one-standard-deviation increase in NCA enforcement is accompanied by a 1.4 percent reduction in wages. This is an especially notable finding if you consider the claim that NCAs incentivize worker training, as that would lead you to expect higher pay where NCAs are more prevalent.

The good news is that some states are taking action against NCAs. Oregon doesn’t allow non-competes for workers who make less than the median family income, for example, and New Hampshire and Oregon both require employers to notify job applicants about NCAs before those prospective employees have officially taken a position. That’s important because more than a third of workers are asked to sign non-competes after a job offer. Courts in Montana and New York have voided NCAs when employees are terminated without cause and several states, including Colorado, Delaware, and Texas, have restrictions on the use of NCAs in health care occupations. California, where Silicon Valley was known for generating NCAs, has rendered most of them unenforceable altogether. Yet 22 percent of California workers there have still reported that they’ve signed NCAs, so there’s more work to be done here.

These state actions all look useful to varying degrees, but a simple piece of federal action could go a long way here. Since low-wage workers should not have to—cannot afford to—sacrifice their ability to pursue higher pay, and since such workers are least likely to possess trade secrets, the federal government should consider a ban on NCAs below some salary or wage level. For example, while any level would be arbitrary, the bottom third of salaries, up to $22,000 today, might be a reasonable cutoff.

While non-competes may make sense in some instances, common sense would dictate that a) most workers do not possess trade secrets of any value, and b) there are better, less coercive ways for firms to retain their workforce. Employees who “feel involved in, enthusiastic about and committed to their work” are much less likely to leave their companies even when offered raises as high as 20 percent, and those who “exhibit high well-being” are “59% less likely to look for a job with a different organization in the next 12 months.”

As regards worker training, economists have long recognized that there’s a potential market failure here. Firms that fear the sunk costs of training will be unrecoverable if workers leave shortly after getting trained will tend to do too little of it. If enough firms think that way, a suboptimal amount of training will be on offer. The classic solution is to make worker training a “public good,” and, in fact, we see some of that occurring with publicly supported community college training initiatives tied to in-demand jobs.

Competition is the hallmark of capitalism, and the bar for restricting it, especially among lower-paid workers who stand to benefit most from competition for their services, should be very high indeed. From that perspective, taking action against NCAs is low-hanging fruit.