A major review of vaccines suggests the AstraZeneca jab does raise the risk of blood clots and another serious condition that can cause bleeding.
But the study found the risk of such problems following a coronavirus infection was still much higher.
The University of Oxford-led team also found an increased risk of stroke after the Pfizer jab - but again at a much lower rate than after infection.
The team said it once again showed the "substantial" benefit of vaccination.
It comes after a coroner ruled on Thursday that BBC Radio Newcastle presenter Lisa Shaw died because of complications from the AstraZeneca jab.
The 44-year-old died in May after developing headaches a week after getting her first dose. She suffered blood clots in the brain.
The research team looked at records from more than 29 million people who received a first dose of a Covid vaccine between December and April, as well as nearly 1.8 million who were infected with the virus.
The study, published in the British Medical Journal, looked for complications up to 28 days after being jabbed or infected.
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