Looking for something new to throw on the grill this Fourth of July? How about a sizzling Denver cut or a couple juicy slices of teres major?

Never heard of them? You will. They’re lesser-known — and less-expensive — cuts of beef that have become more popular as tough economic times have led butchers to look for tenderness at a lower price than the classic rib eyes and tenderloins.

“I call them the cuts of our ancestors,” says Pat LaFrieda, a third-generation butcher who appears with his father on the Food Network show “Meat Men.” ''All the cuts that I remember eating as a kid with my grandfather, those are the cuts that I see restaurants asking for again; it fits into their price schedule.”

Running Pat LaFrieda Meat Purveyors, LaFrieda, his dad Pat Sr., and cousin Mark Pastore supply more than 500 customers, including some of the top restaurants and bistros in New York City, which gives him a heads up on culinary trends. “What they’re asking for today, I know I’ll start seeing in butcher shops six months from now.”

Want to know what kinds of meat you’re likely to meet over the next few months? Here’s a rundown from LaFrieda and other enthusiasts.

Denver cut: Kari Underly, a third-generation butcher and author of “The Art of Beef Cutting,” was part of the team that developed the Denver cut and flat iron steak for the beef industry. Profiling muscles and analyzing cuts such as chuck and round is irresistible to “a meat geek like me,” says Underly, who likes to “dig through the data and find the little gems.”

The Denver cut is found in a part of the cow typically sold as chuck roast, but when cut separately it is the fourth most tender muscle, Underly says.

For the Denver cut, she recommends having it sliced about three-quarters of an inch thick. Try a lightly flavored marinade or a rub; the meat doesn’t really need to be tenderized, just flavored. Then grill, possibly throwing some baby bok choy on the grill with it to balance the protein.

Teres Major: This is a familiar cut to chefs. It’s a little-used muscle in the cow’s shoulder, second only in tenderness to the tenderloin, but about half the price.

Charlie Palmer, a leader in the chef-turned-butcher movement, has been featuring teres major steaks at his District Meats in Denver and Burritt Tavern in San Francisco.

“It’s just as tender as filet mignon, but half the price. And our guests like to say the name!” he says. He serves it with torpedo onion confit, which is similar to a scallion but has a bronze-red bulb at the base and a mild flavor. For the meat, he recommends keeping it simple. Cook on a hot grill until medium rare, let it rest, then slice into medallions.

Chuck roll steak: This is a newer cut that is being separated out from the more common chuck roll, which usually is sold as the boneless chuck roast.Prepare as a rib-eye, with a short marinade, salt and pepper, and a simple grilling.

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