This piece was updated Wednesday afternoon to include a statement from Amazon.

Other companies have good reason to be unhappy with Amazon’s plan to lobby the government for a $15 minimum wage after increasing its own wages. But some Amazon employees themselves take issue with the plan. The new minimum wage comes with a cut to the benefits that the company once offered. For some workers, that actually amounts to a pay cut.

That points to a complicated problem that advocates of raising the minimum wage don’t have an answer to: Wages are just one form of compensation.

When Amazon announced that it would be paying its workers more, it quickly drew a wave of support both within the company and from political supporters of raising the minimum wage like Bernie Sanders who cheered the effort.

Clearly, some employees, including seasonal staff hired to meet holiday demand, have a lot to gain from Amazon’s new plan.

For other, long time employees, however, an hourly pay raise may well mean lower take home pay. That’s because Amazon will no longer give employees stock options and monthly bonuses. Although that income wasn’t part of a minimum wage, it did add significantly to worker’s pay.

[Related: Minimum wage hikes don't help poor people]

These bonuses, however, are variable and are often harder to understand than the single number of an hourly wage. And Amazon’s system wasn’t the most straight forward. For one thing, workers in different parts of the country made different amounts. For another, bonuses included various provisions such as productivity, attendance and extra holiday bonuses that in some cases allowed employees to earn 16 percent on top of their base wage.

That means that for all of Amazon’s claims that the boost in hourly wage “more than compensates” for other income, that’s actually a hard claim to quantify.

Even Sanders, who was quick to give his support to the company, has since asked for clarification about the compensation provided to employees who once counted stock options as part of their pay.

But this should be a lesson for those who demand a higher minimum wage. Just because a number looks nice on a sign and is easily understood doesn’t mean that it’s a better deal for workers.

Indeed, Washington D.C. learned this the hard way. A ballot proposal supporting boosting minimum wage passed only for the liberal city council members to reject it because the misleading language actually didn’t help the workers that the proposal claimed to help. It also would have been a hit for the city’s vibrant restaurant industry.

Minimum wage is much more complicated than its advocates make it out to be. Voters and lawmakers should pick the more difficult task of actually understanding the impact of such proposals for workers, the country and the economy, rather than just going for good looking numbers for protest signs.

Amazon, however, defends its decision, saying in a statement: "All hourly Operations and Customer Service employees will see an increase in their total compensation as a result of this announcement. The significant increase in hourly cash wages effective November 1 more than compensates for the phase out of incentive pay and future RSU grants."

The company added, "In addition, because it’s no longer incentive-based, the compensation will be more immediate and predictable. Employees who have previous grants that are vesting in 2019 and 2020 are keeping those grants, so they will benefit from both the value of those shares when they vest and the new increase in cash compensation. Some employees have benefited from a bull market and the unusually strong appreciation of Amazon’s stock price in recent years. This is a good outcome for those employees, but such stock price appreciation is by no means guaranteed to continue. Stock markets and individual stocks can go up, but they can also go down. For employees who want to invest in stock for the possibility of future growth, we will be rolling out a direct stock purchase plan in 2019. We are continuing to roll out the details of all these changes to employees this week."

Time, however, will tell if Amazon's decision to change it's pay scheme will actually leave workers better off. Right now, there is plenty of reason to be skeptical.