Let’s admit one thing up front: covering Amazon for a newspaper owned by the company’s founder, Jeff Bezos, has to be almost impossible. Even though Bezos has made it clear he has no interest in micro-managing what The Washington Post writes about, and executive editor Marty Baron has repeatedly said he never hears from Bezos about editorial matters, the Amazon CEO’s ownership of the paper is constantly in the forefront of people’s minds. Of course, Donald Trump keeps trying to make it an issue, but it also comes up when the Post writes about news events that involve Amazon. The paper is usually quick to disclose the conflict, but that isn’t always enough to dispel a sense that it sometimes pulls its punches.

Take a recent story about a review of the US Postal Service and the rates it charges third-party shippers. The review was sparked by concerns that the postal system is too beholden to Amazon; Amazon relies on USPS to handle almost half of its packages. (Needless to say, this is a controversial issue. Trump claims the USPS loses money on its Amazon deliveries, despite the fact that the Postal Regulatory Commission says the USPS is at least breaking even on all its shipping contracts.) Comparing the Post‘s coverage of the story with The Wall Street Journal’s coverage shows a somewhat different tone in the Post story, one that appears to downplay Amazon’s role in the controversy.

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The Journal‘s headline was “Postal Service Review Proposes Sweeping Changes Likely to Hit Amazon.” The lede paragraph said a Treasury-led task force was proposing the postal service charge more for certain deliveries, and that it was “going after Amazon.com Inc. and other online retailers.” The Post, meanwhile, went with a headline that said “Treasury suggests review of postal rates – but not just for Amazon.” The lede paragraph said the task force evaluating the postal service was recommending a slew of options, “but did not go so far as to say the financially strapped Postal Service is losing money to Amazon, a company which contracts services from the Postal Service.”

The Journal story notes at the beginning that “higher rates on package services would hit Amazon, which Morgan Stanley estimates relies on the Postal Service to deliver up to 45 percent of its packages.” The rest of the story describes the background to the fight—including the fact that the USPS is $62 billion in debt—but it is clear Amazon is a central focus of the report. This makes sense, since its contract with the postal service is the main reason Trump commissioned the review. The Post story, by contrast, doesn’t mention Amazon again until the very end, when it points out the review “has been viewed as an official action taken to penalize the company,” and later notes that Postmaster General Megan Brennan told Trump “the Postal Service benefits from its contract with Amazon.” A spokesperson for the Post says they could see “no substantive differences” between its story and the one published by the Journal.

This isn’t the first time the Post has faced criticism over the way it handles Amazon. The paper mentions toward the end of its postal service story that Bezos owns it, but it doesn’t always do this. According to a recent piece in Counterpunch, the paper’s ties to the company weren’t disclosed in a number of stories, including one that involved political lobbying and quoted a source who mentioned Amazon, and another that referred to the Federal Trade Commission and potential regulation of companies like Facebook, Google, and Amazon. The Post spokesperson said the paper’s policy is to mention the ownership whenever the company is mentioned “in anything but the most glancing way that raises no questions of a possible conflict.”

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In a recent HuffPost story that asked Post employees to share their thoughts about being owned by Bezos, there were definitely suggestions that the potential conflict between Amazon’s CEO and the paper is something staffers think about. “I would say that I tend to do less critical thinking about Amazon than I do, say, about Facebook or Google or Walmart, and the reason is fairly obvious: because I am thankful for the opportunity I have, which wouldn’t exist without Jeff Bezos,” said one employee. Is there any evidence to suggest that the Post‘s coverage of the postal service story was deliberately more favorable to Amazon? No. But a newspaper’s ownership can influence coverage in more subtle ways than outright calls for censorship, including self-censorship and the pulling of punches. And the price of being owned by one of the world’s richest men is that some will inevitably see bias even where it might not exist.

Correction: An earlier version of this post referred to Marty Baron as the editor in chief of The Washington Post. He is the executive editor.

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Mathew Ingram is CJR’s chief digital writer. Previously, he was a senior writer with Fortune magazine. He has written about the intersection between media and technology since the earliest days of the commercial internet. His writing has been published in the Washington Post and the Financial Times as well as by Reuters and Bloomberg.