More good news on progress towards an escape route from this pandemic: On Monday, vaccine researchers from Oxford University and the pharmaceutical company AstraZeneca announced results from a “Phase 1/2 trial,” suggesting their product might be able to generate immunity without causing serious harm. Similar, but smaller-scale results, were posted just last week for another candidate vaccine produced by the biotech firm Moderna, in collaboration with the U.S. National Institutes of Health.

As both these groups and others push ahead into the final phase of testing, it’s vital that the public has a clear and balanced understanding of this work—one that cuts through all the marketing and hype. But we’re not off to a good start. The evidence so far suggests that we’re getting blinkered by these groups’ PR, and so seduced by stories of their amazing speed that we’re losing track of everything else. In particular, neither the mainstream media nor the medical press has given much attention to the two vaccines’ potential downsides—in particular, their risk of nasty adverse effects, even if they’re not life-threatening. This sort of puffery doesn’t only help to build a false impression; it may also dry the tinder for the future spread of vaccine fear-mongering.

Back in May, a CNN report described the Oxford group as being “the most aggressive in painting the rosiest picture” of its product, so let’s start with them. Just how rosy is the Oxford picture really? It’s certainly true that this week’s news shows the vaccine has the potential to provide protection from Covid-19. But there are flies in the ointment. After the first clinical trial for this vaccine began in April, for example, the researchers added new study arms in which people got acetaminophen every six hours for 24 hours after the injection. That’s not featured in their marketing, of course, and I saw no discussion of this unusual step in media coverage in early summer. Newspapers only said the vaccine had been proven “safe with rhesus monkeys,” and did not cause any adverse effects in those animal tests. It was a worrying signal though: How rough a ride were people having with this vaccine? Was the acetaminophen meant to keep down fever, headaches, malaise—or all of the above?

The Oxford group is also giving acetaminophen to participants in an advanced, phase 3 trial now underway in Brazil, too. In another major study of the vaccine, involving 10,000 people in the UK, you can’t participate if you have an allergy or condition that could be made worse with acetaminophen. No mention of the extra drug, though, in the same group’s trial in South Africa.

Journalists could have pressed them on this issue months ago. The first people to get vaccines are carefully picked to be the least likely to have a negative reaction. If the Oxford vaccine is knocking them around badly, it might not bode well for the rest of us. Don’t get me wrong: a day or two of pain or illness wouldn’t deter me from getting an effective Covid-19 vaccine. But I think we need to be prepared if that’s going to be the case.

The press release for Monday’s publication of results from the Oxford vaccine trials described an increased frequency of “minor side effects” among participants. A look at the actual paper, though, reveals this to be a marketing spin that has since been parroted in media reports. (The phrases “minor side effects” or “only minor side effects” appeared in writeups from the New York Times, the Wall Street Journal and Reuters, among other outlets.) Yes, mild reactions were far more common than worse ones. But moderate or severe harms—defined as being bad enough to interfere with daily life or needing medical care—were common, too. Around one-third of people vaccinated with the Covid-19 vaccine without acetaminophen experienced moderate or severe chills, fatigue, headache, malaise, and/or feverishness. Close to 10 percent had a fever of at least 100.4 degrees and just over one-fourth developed moderate or severe muscle aches. That’s a lot, in a young and healthy group of people—and the acetaminophen didn’t help much for most of those problems. The paper’s authors designated the vaccine as “acceptable” and “tolerated,” but we don’t yet know how acceptable this will be to most people. If journalists don’t start asking tougher questions, this will become the perfect setup for anti-vaccine messaging: Here’s what they forgot to tell you about the risks…