Coral reefs where lots of different kinds of fish swim are healthier than overfished ones, scientists have shown.
Researchers showed a reduced incidence of coral disease in areas of the Philippines where fishing is banned, compared with neighbouring areas.
They conclude that some types of fish probably carry coral diseases.
Writing in Proceedings of the National Academy of Sciences (PNAS) they suggest that when predatory fish are absent, disease-carrying species thrive.
Members of a family called butterflyfish (Chaetodontidae), which are not caught for food, appear the likely culprits in disease transmission.
"People like to eat the big predators such as groupers and a few others," said lead researcher Laurie Raymundo.
"In some cases [on the reefs we studied] these species are not so abundant, and in others they've just gone.
"And the general trend is that where you find more functional diversity, you find fewer butterflyfish," the University of Guam researcher told BBC News.
Coral diseases have inflicted substantial damage in a number of regions in recent years, notably the Caribbean, where naturally abundant species such as elkhorn and staghorn have been almost wiped out in some places.
The causes of the six diseases in Dr Raymundo's study are not all known, but are thought to include bacteria and viruses.
The researchers selected seven marine protected areas (MPAs), mostly just a few hectares in size, where fishing has been banned for at least five years, and seven neighbouring areas with the same underlying ecology.
In every case, the fished sites showed a higher incidence of disease - double, in some cases.
The researchers found an unusually high abundance of butterflyfish on heavily diseased reefs; and that butterflyfish numbers fell when there were lots of other types of fish around.
Many butterflyfish species feed on coral, and that is perhaps how they transmit disease.
The researchers subsequently scoured a database on coral conditions on Australia's Great Barrier Reef, and found similar patterns.
The relationship between coral disease and other environmental issues is complex.
Disease seems to be exacerbated by pollutants such as sewerage and fertiliser, and may be stimulated by anything that stresses coral, such as the abnormally high water temperatures seen in East Asia during El Nino years.
Australian researchers have argued that protecting the diversity of reef life could provide a partial defence against climate impacts, by keeping corals generally healthy and enhancing their capacity to cope with rising temperatures.
Dr Raymundo's work is making the case for protecting marine life, particularly the big predatory fish beloved of fishermen and fish-eaters, in order to keep reefs healthy - although that might not mean banning fishing entirely from such areas.
"One of the things that came out of this is that if you have a well-managed MPA, it works to keep coral healthier," she said.
"But even on reefs that are fished, if you can maintain diversity you still have that effect on coral health.
"So as long you keep certain species there and can control fishing - don't catch in certain seasons or don't catch fish under a certain size, whatever is appropriate - you might not have to ban it completely."