“Flauta” means “flute”—implying something long, round, and slender—but some of Austin’s finest flautas challenge the definition. Manuel’s does splendid, and unusual, grilled flautas: Toasty-crisp, these folded-over corn tortillas are filled with chicken and served with verde or ranchera sauce and a splash of sour cream; the blocks of intense color at the restaurant’s northwest Austin dining room evoke modern Mexico, while the slick downtown venue is contemporary American. At the humble Burnet Road location of Taquerias Arandas—decorated with not one but two murals of Jalisco scenes and frequently packed at peak times—a folded corn tortilla filled with chicken makes a superior, grilled flauta, non-greasy and almost airy. Big, commercial, and efficient, Matt’s El Rancho is full of surprises; for one, it offers grilled (not fried) flautas, crispy from the griddle and stuffed with chicken.

Surprise: You’ll find Dallas’s best flautas at refined, fashionable La Duni, which gives this modest dish the star treatment. A quartet of smallish, crunchy fried-tortilla cylinders filled with hand-pulled roasted chicken and bits of cilantro and tomato are served with a lush roasted-tomato salsa and a bit of average creamed guacamole; a salad of greens, spinach, and watercress gives the plate extra pizzazz. Much more rooted in tradition, the flautas at come-as-you-are Herrera’s are a burly pair for hearty appetites. Big, long, and packed with chunks of chicken, the freshly fried rolls are just right for dredging in some guacamole, sour cream, and salsa.

The shredded-beef flautas at Forti’s Mexican Elder, a local favorite with a high-ceilinged indoor courtyard, are not the usual long, thin tubes but instead are long (two overlapping tortillas) and fat; for once, the crunchy tortilla doesn’t overwhelm the filling. Guacamole and sour cream come on the side for dipping.

At Joe T. Garcia’s, you can order flautas from the menu at lunch or by request at dinner. These small, brittle, cigar-size rolls are filled with scantly seasoned, coarsely chopped chicken. Dredged in a little of Joe T.’s excellent guacamole and then dipped in the rich table salsa, they are perfection.

You’ll find the finest flautas in town at sunny, Mexican-ceramics-filled Sylvia’s Enchilada Kitchen, in west Houston. Little flautitas are stuffed with moist shredded chicken breast and served with cool sour cream and buttery guacamole salad; they’re only improved with a splash of warm salsa. A close second are the dainty, pencil-thin chicken flautas artistically drizzled with sumptuous avocado-and-sour-cream sauce at Gorditas Aguascalientes, a rustic mainstay that is an outpost of central Mexican cuisine; aguas frescas, the fresh Mexican fruit drinks, are exemplary here. Fried tortilla chips and flautas are the crispiest ever at charming Maria Selma’s, where mildly seasoned duck-filled flutes are painted with crema and the menu features Mexico City–style cuisine.

At La Mexicana, a bare-bones cinderblock building with a noisy clientele, the flautas, each made with two overlapping corn tortillas, are stuffed with shredded chicken (or chunks of breast) or ternera (shredded beef) and—a novel touch that makes a big difference—topped with sautéed onions, tomatoes, and bell peppers.

Spunkily flavored chicken fills the crisp, freshly fried flautas, made with thick corn tortillas, at Costa Messa, McAllen’s retreat when you want a place to dress up a bit and curry favor with your spouse or the boss. A series of sprawling rooms that really jump when a couple of mariachi bands are going full blast, Poncho’s, in Pharr, excels at chicken flautas, fried to a golden turn and served with a terrific and atypical blended salsa chimichurri made from ancho chiles, jalapeños, avocado, olive oil, and sour cream.

The chicken filling has a sweet, oniony tang and the rolled tortillas are crisply fried—the city’s best flautas are served in Tito’s big, simple dining room with its array of quirky local art. The tightly rolled chicken flautas at Picante Grill are exceptionally crunchy and not a bit greasy; families and couples fill up the dining rooms, which are brightened with paper flowers and angular still lifes.