One reason I love Christopher Guest’s series of mock-documentaries is that nearly all of them take as their subject different kinds of pop music: “This Is Spinal Tap” with heavy metal, “Waiting for Guffman” with ersatz Broadway, and “A Mighty Wind” with folk. (“Best in Show,” the Guest film that isn’t musical, also treats a topic dear to my heart.) Most of these films involve Michael McKean in a dual capacity as actor and composer.

Now for the first time in a New York cabaret, Mr. McKean has assembled an hour’s worth of his songs, many of which were co-written with his wife, television actress Annette O’Toole, along with her daughter (from a previous marriage), Nell Geisslinger. Mr. and Mrs. McKean and Ms. Geisslinger alternate between singing leads and accompaniments, and switch between various guitars, mandolins, a piano, and even an “authentic Celtic drum made in an Irish neighborhood in Kenya” (Kenya beat that?).The result is a generally delightful program called “No Standards,” which plays at Feinstein’s until June 4.

Born in New York in 1947, Mr. McKean grew up amid the folk-pop (and then the folk-rock and singer-songwriter) of the 1960s, and most of his songs are written in those idioms, with varying degrees of irony. Some songs are complete comic parodies of folk music; others are totally straight; still others fall somewhere in between. When the trio started each new piece, there was a hesitant air among the crowd, as we silently asked one another, “Well, do we laugh at this song, or don’t we?”

“The Good Book Song” ridicules over-the-top Bible thumpers while “She Sings Hymns Out of Tune,” despite the comic possibilities evident in the title, is apparently a serious character study. “Killington Hill” parodies bloodthirsty traditional songs of murder (e.g. “Tom Dooley”), with lines like “Oh ’tis pity I’m thus mutilated.” By contrast, “Buried on Page Four,” which begins with a woman being killed in a train accident, is no laughing matter.

Some of the material is very inside baseball. There were a number of Hollywood in-jokes I didn’t get, and my companion had to explain to me that the central reference in “Groton Farewell” is to a prep school. Much humor is added if you know the films – the gently psychedelic “Cups and Cakes” is performed by “The Thamesmen” (the supposed antecedents of Spinal Tap) and “A Kiss at the Rainbow” is used in the climactic sequences of “A Mighty Wind” – yet the songs are entertaining in themselves.

While the performers take a few of their own numbers seriously, they don’t do the same for the two standards they include, both by Johnny Mercer. “I Remember You” is lightly comic, with Ms. O’Toole singing over minimal guitar chords and Ms. Geisslinger making goofy percussion noises with her cheeks a la Fritz Feld. The more obscure, folksy “Down T’Uncle Bill’s,” has Mr. McKean singing straight while the two ladies, unbeknownst to him, undulate through an increasingly elaborate series of timesteps behind him.

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Brian Stokes Mitchell’s “Love/Life,” could be called “All Standards.” Mr. Mitchell is almost inarguably the greatest currently active Broadway leading man, as he proved with triumphant performances in the recent revivals of “Kiss Me, Kate” and “Man of La Mancha.” With this one-man show, Mr. Mitchell eschews traditional Broadway material in favor of jazzy treatments of standards from the Great American Songbook. He is one of the few Broadway singers who could hope to make the transition, and does so brilliantly.

His opening number, “It’s All Right With Me,” stops the show almost as soon as it starts. From this moment on, Mr. Mitchell shows that he is one of the few who understands the difference between the way he sang Cole Porter in “Kate” and the way Sinatra or Tony Bennett sing Cole Porter. When you sing without a costume (other than a tux or a suit), your chief assets are rhythm, interpretation, and personalization, making your version of a well-known song different from anyone else’s.

Mr. Mitchell’s version, playing Sundays and Mondays on the set of “The Light in the Piazza” at the Vivian Beaumont Theater, generally avoids the pitfalls of both the neck-busting Broadway belter and the smarmy Vegas lounge lizard. To be sure, he sometimes tries too hard: There’s a long treatment of another Porter classic, “Love for Sale,” in which he overindulges in a soulful stance and odd-meter funk, and in a few ballads he gets a little too croony.

But more often, Mr. Mitchell shows great taste in arrangements (some by musical director Gerard D’Angelo) and shows he knows how to get the most out of them. A wonderful series of jazz adaptations of the “My Fair Lady” score by John Williams, originally done for drummer Shelly Manne’s band, include “Show Me” rendered with Afro-Cuban polyrhythms, and “I’m an Ordinary Man” sung (not spoken, as it was by Rex Harrison) as if it were a love song, with the melody moving in and out of 6/4.

Mr. Mitchell makes his point: He can do this kind of music as well as he does traditional Broadway fare. I wouldn’t mind, however, seeing him do a one-man show or even an album of leading-man songs in the future. He is never more convincing here than in a segment that begins with a personal reminiscence of his early days in New York. This leads into a treatment of “Take the ‘A’ Train” in which he sings the rare Delta Rhythm Boys lyric while the quintet (featuring Bob Cranshaw, best known as Sonny Rollins’s bassist) plays “Another Hundred People” from “Company.” Then, he takes us all by surprise by singing the Sondheim classic while the group plays “‘A’ Train” in the background. Would that New York life were always so tuneful and harmonious.

Michael McKean until June 4 (540 Park Avenue, at 61st Street, 212-339-4095).