The United States Fish and Wildlife Service is now exploring where it might be helpful. Models suggest that commercial harvest of Asian carp in the Mississippi would most likely help control populations there, “as part of an integrated pest management program,” said Valerie Fellows, a spokeswoman.

In practice, it is still unclear whether commercial fishing pressure could be high enough to have a significant impact, she said. The Army Corps of Engineers has spent millions of dollars to erect electronic barriers to keep Asian carp from moving from the Illinois River into the Great Lakes.

There are risks to whetting America’s appetite. Marketing an invasive species could make it so popular that “individuals would raise or release the fish” where they did not already exist, Ms. Fellows said, potentially exacerbating the problem; tilapia were originally imported into Latin America for weed and bug control, but commercialization helped the species spread far more widely than intended.

Dr. Kramer is concerned that the marketing of lionfish might increase the number of traps on reefs, which could trap other fish as well. He said spearfishing was the sustainable way to catch lionfish, which are reef dwellers.

Cookbooks do not say much about how to filet an Asian carp, which has an unusual bony structure. And even if one developed a taste for, say, European green crab soup, there is nowhere to buy the main ingredient, though it is plentiful in the sea.