The way you avoid any problem with refreezing is to buy it frozen in the first place. If you're more than, say, 50 miles from a coast, that's the only way to assure quality fish at all.
I know that "frozen" seems to be treated like a four letter word. But, in fact, frozen is not only more common, it is the best quality when handled properly.
Let's compare.
Unless you meet the day boats at the dock and buy the fish right off the deck, so-called "fresh" fish, when you buy it, is several days old. Starting on the boat, the fish was caught anytime from today, to three days ago, and kept on ice. It is then landed, where a processor buys it from the boat. The fish is cleaned, butchered if necessary, and otherwise processed. A wholesaler then buys it from the processor, and delivers it to you, if you're a restaurant, or to a fish market. You, as a retail customer, then go into the market and buy it. Minimum elapsed time: four days, which can stretch to a week. And that's just with locally caught fish. With imported fish it can be even longer.
Example: During the Copper River season, my fish monger identifies when the fish was air-shipped. For instance, when I shop on Thursday or Friday, the tag might say, "air-shiped Tuesday (date). Even assuming the fish was processed on the same day it was shipped, that makes it three or four days old. Odds are we can add
at least another day for the netting and processing.
How fresh is that?
FAS fish, on the other hand, is caught, immediately processed, and flash frozen. Elapsed time: no more than two hours. Unless you catch it yourself, it doesn't get any fresher than that.
Problems arise not because the fish was frozen, but in how it is handled by the consumer. Fish should be defrosted slowly, in the fridge. Despite what the "experts" say, running it under cold water effects both the flavor and texture (and there's probably a loss of nutrients as well).
You also have to be sure that it is FAS fish. Some unscrupulous fish mongers will freeze slow moving fish on-site, in a regular freezer. They will then sell it to you either that way, or, even worse, defrosted.
FWIW, by law, previously frozen fish that's been defrosted is supposed to be identified as such at the fish counter. Most reputable fish places go further than the law, and the ID tags, in addition to the price, will include info such as "wild caught," "farmed," "previously frozen," "local" etc.
- Be very wary about freezing fish from the market, because re-freezing is disastrous for texture;
This is problematical at best. Conventional wisdom has it to be a great truth. But is it?
Freezing fish in a home freezer can be the culprit, no matter how fresh the fish may be. Home freezers are slow working, and large ice crystals form. Then the fish is defrosted improperly, which increases the problem.
I would suggest that most of the time a piece of FAS fish that's been properly defrosted, then refrozen in a home freezer, will end up with the same texture as one that started out fresh and was frozen the same way.