For environmental groups like Oceana, the Center for Biological Diversity and the Turtle Island Restoration Network — all of which fought for the new law — this equals progress.

Even if you've already sworn off of eating taboo items like bluefin tuna, Chilean sea bass and shark, you may still be contributing to the global bycatch tally. Following are a few seafood items to approach cautiously the next time you're thinking fish for dinner:

A halibut is seen on the line of a fisherman in Ilulissat, Greenland. Photo: Joe Raedle/Getty Images

California halibut: "Local" does not mean "sustainable," as seen in the nearshore halibut fishery of California. A 2010 survey of just 12 percent of the total gillnets used to catch halibut found that 25 sea lions, three harbor seals and a dolphin were also entangled. All had drowned. These same nets, meanwhile, caught 94 federally protected great white sharks from 2006 to 2011, with many of them dead, according to the state's Department of Fish and Wildlife.

Seventy percent of the total catch by weight is discarded at sea by California halibut gillnetters. Trawlers — who drag nets along the bottom to scrape up their catch — are just as destructive. From 2002 to 2009, halibut trawlers in Monterey Bay tossed back about 70 percent of their total catch, according to state and federal data compiled by Oceana. Much of the bycatch consisted of dead and injured sharks, rays, Dungeness crab and jellyfish.

Good alternative: Halibut caught with rods, reels and single hooks. Ask your fish vendor or server who caught their halibut, where and how. If they don't know, order something else.

A fisherman checks the measurements of a Dungeness crab he just pulled in from the Pacific Ocean off Marin County, Calif. Photo: Eric Risberg/AP

East Coast lobster, West Coast crab: Lobster and crab are by and large good choices. The stocks are generally healthy and well managed, and bycatch is minimal.

Thing is, whales can get tangled in the cables that connect lobster and crab traps to buoys at the surface. Between 1980 and 2004, 73 percent of a population of 493 Atlantic right whales were snared in lobster trap cables at least once – with some whales showing evidence of six incidents -- according to a 2012 article published in the Journal of Marine Biology. The same authors reported that, in Southeast Alaskan waters, at least 52 percent of humpback whales have been tangled at least once in crab trap cables. The whales sometimes die; for those that live, the wounds and scars remain for years.

Good alternative: Massachusetts lobstermen are required to use sinking lines that hug the bottom and make the water above safer for whales, while other trap fishermen are experimenting with colorful, high-visibility lines to help avoid whale entanglements. Before you buy your next lobster or crab, ask about the creatures' origin and the gear used to catch them.

A swordfish chills on ice. Photo: PA Photos /Landov

Swordfish: Gillnets, draped beneath the surface like deadly curtains, entangle nearly every other swimming creature too big to slip through. Off the coast of California, swordfish gillnets during the 2010-2011 season killed 27 ocean sunfish (also called mola mola), three thresher sharks, two mako or blue sharks and five opah for every swordfish landed. The same fishery caught at least two sperm whales in 2010 — killing one of them — and total marine mammal deaths are more than 100 per year, according to federal fisheries managers. The death rate for marine mammals in these gillnets is almost 100 percent.

Good alternative: Harpoon-caught swordfish. Some swordfish are hunted by harpoon. Swordfish caught by this method is a specialty item, expensive enough that your waiter or fish vendor will be sure to tell you how it was taken — and swordfish not sold as such likely came from a gillnet or a longline.

A fisherman holds freshly caught potted brown shrimp in Southport, United Kingdom. Photo: Christopher Furlong/Getty Images

Shrimp: Perhaps no fishery is more destructive than the global shrimp trawling industry, which wastes more than six pounds of marine life for every four pounds of landed shrimp, according to the United Nations Food and Agriculture Organization. But in Mexico's Sea of Cortez, it gets much worse than that.

A study published in the science journal PLOS One in 2012 reported that sandy bottom trawls targeting shrimp wound up with bycatch rates as high as 97 percent. The lead author, Lorayne Meltzer, of Arizona's Prescott College, estimated that in 2009, shrimp trawlers working just a portion of the Sea of Cortez caught (and mostly killed) almost 74,000 tons of unwanted bycatch. Meltzer told us that farm-raised shrimp aren't a good alternative for the eco-conscious, either. Shrimp farms, Meltzer says, cause massive coastal deforestation, pollution and erosion, often turning tropical estuaries into muddy wastelands saturated with shrimp effluent and antibiotics.

Good alternative: Most shrimp sold in the United States is either trawled off the bottom or farmed in Indonesia — so shop cautiously. Your best choices include farmed shrimp from the United States, Oregon pink shrimp and Pacific Northwest spot prawns.

An Almadraba tuna is lifted by a crane in the port of Barbate, Cadiz province, southern Spain. Almadraba tuna is caught by an elaborate and ancient Andalusian fishing method used in Spanish coastal areas close to the Strait of Gibraltar since Phoenician times. Photo: Emilio Morenatti/AP

Tuna: Tuna fishermen don't only catch tuna. In fact, they mostly don't catch tuna-- especially when they use longlines rigged with hundreds of baited hooks. A recent study commissioned by the Food and Agriculture Organization found that tuna fishermen hauled in 750,000 tons of tuna and 828,000 tons of non-tuna creatures per year in the mid-2000s. In some regions, a quarter of the total catch is sharks, according to a report published in 2007. Many sharks are thrown back dead — including 20,000 tons of blue sharks annually in the North Atlantic, as reported in the Marine Ecology Progress Series.

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