Those dimensions — a mouth 5cm wide trying to swallow a fish 10cm wide — would seem to present a problem.
But as we watched with horrified fascination, gradually, a few millimetres at a time, the broad body of the reef fish disappeared inside, until finally it vanished.
I was sufficiently excited by watching this gruesome sight to look around to check for any big predators that might feel inclined to do the same to me.
There were a few reasonable-sized fish hovering around the clumps of coral, but they all had the comforting, round shapes of the fish we like to eat rather than the streamlined form of the ones that might like to eat us.
Like the rest of my scuba dive at Tikioki — one of the growing number of marine reserves being established by the Cook Islands — everything was very gentle and relaxed. And that made it perfect for my first serious scuba outing since a heart attack five years before.
We didn't even have to roll off a boat, just walk down the sandy beach into the calm waters of Rarotonga's lagoon, and the first fish were right there.
I can't say I had great expectations, because I had snorkelled in this same area during a visit to the Cooks seven years before and had been disappointed.
But designating the area as a raui, or marine reserve, had obviously helped because there were lots of brightly-coloured reef fish, of which the few varieties I was able to recognise included schools of nervous butterfly fish swarming round their coral havens, goatfish using their strange chin whiskers to feed on the bottom, marvellously patterned parrotfish grazing on the coral, stroppy little damselfish trying to chase us away from their patches and a weird-looking big blue fish, which I think was a hump-headed Maori wrasse.
The coral was better than I remembered, too, with plenty of staghorns, a few of the appropriately-named table corals and a lovely yellow variety I don't know the name of. Nga also pointed out some giant clams, a massive moray eel with some very nasty looking teeth and a small octopus strolling across the sand.
It wasn't a spectacular dive — for that I'd have had to go outside the reef — and it wasn't as lovely as the snorkel trail I had followed off Pacific Resort Aitutaki a few days before, but it was definitely worth the effort.
Afterwards, I asked Nga if he thought the marine reserve was making a difference. "Yes, it is getting a bit better every year," he said.
That's good news because, as I later discovered in a conversation with Cook Islands Prime Minister Henry Puna, there are plans to make things even better.
For a start, the Government of the Cooks and the New Zealand Aid Programme have launched a $3 million project to improve water quality in the lagoons around Rarotonga and Aitutaki, starting with the Muri area. The first stage, already underway, involves upgrading septic tank systems at 200 homes around the edge of the lagoon.
The Cook Islands is also working towards creating a 1 million sq km marine park — the biggest in the world — around its southern islands.
Puna said this would be modelled on Australia's Great Barrier Reef Marine Park with zones for fishing, tourism and recreation but also a strong emphasis on "ocean conservation management ... that takes account of raui currently in place and the connections between the shore, reef and ocean environments."
If all of that comes to pass, then next time I go for a dive in the waters around Rarotonga it should be even better than it is now.
CHECKLIST
Getting there: Air New Zealand flies from Auckland to the Cook Islands six times a week. Air Rarotonga has links to many of the other islands.
Accommodation: Pacific Resort Rarotonga is on the lovely Muri Beach.
Further information: cookislandsdivers.com, cookislands.travel.
Jim Eagles visited Rarotonga with help from Cook Islands Tourism, Air Rarotonga and Air New Zealand.
