There are two types of cabaret singers you’re likely to come across in the major rooms of New York. First are the pure cabaret performers who earned their reputations doing one-person shows in small rooms; the standard-setters in this category are Mary Cleere Haran, Michael Feinstein, and Andrea Marcovicci, the latter of whom began a month-long run at the Algonquin Hotel’s Oak Room on Tuesday night. Then there are the musicaltheater stars transferring their skills to an intimate setting, among them Barbara Cook, Brian Stokes Mitchell, Patti LuPone, and the wonderful Rebecca Luker, who this weekend will wrap up her two-week run at Feinstein’s at the Regency.

The difference between theater people doing cabaret, such as Ms. Luker, and performers who have devoted their careers entirely to this medium, like Ms. Marcovicci, has a lot to do with a type of music that may not, at first, seem to have much in common with either: jazz.The jazz influence on cabaret has little to do with musical values, like advanced harmonies or swinging rhythm, but rather is manifested in terms of an overall concept.

From its earliest beginnings in New Orleans, jazz was distinguished by the concept of interplay, both among musicians and between musicians and their listeners. Cabaret singers don’t scat (thank God) or exchange four bar phrases with their pianists or bassists (again, thank God), but the best of them engage in a constant give-andtake with their audiences. Contrastingly, theater people present a show that is essentially a musical comedy or drama boiled down to one performer’s 75-minute act.

With a theater performer, you feel that it doesn’t matter who’s in the house: They could be putting on the exact same show if the room were totally empty. Cabaret performers, on the other hand, rely on audience participa tion. Ms. Marcovicci is an absolute master at making you think her show would be entirely different if you weren’t there. One of her most successful tactics involves asking crowds to identify the show a certain song comes from – even I fall for that one!

In her current show, entitled “Just Love … By Request,” Ms. Marcovicci brings the concept of audience interaction to a new level. Whereas her other Oak Room shows set songs in the context of an era (World War II), a performer (Fred Astaire), or a composer (Cole Porter), Ms. Marcovicci’s only reference point here is the way in which songs relate to her own life, and to audience members’.

Roughly half the show is pre-set – including one song (“Brave and Foolish Thing”) written for her wedding and another (“Look at Those Eyes”) composed in honor of her daughter. The rest consists of requests, written out on forms left on the tables and gathered into a top hat by the diva herself. Ms. Marcovicci not only asks the audience members to name the songs they most want to hear, she also asks that they explain why the ones they chose mean so much to them – sort of like Phil Donahue, but with more modulations.

One of the show’s standouts is “Umbrella Man,” a goofy novelty from 1939 set in 3/4 time. Here Ms. Marcovicci takes a silly song and makes it sublimely moving, instantly transporting us into another time, another place.

The show also includes two tour-deforce “list” songs. Johnny Mercer’s multi-chorus masterwork “Spring, Spring, Spring,” is delivered in all its elongated glory. Ms. Marcovicci either slows down to emphasize a cute rhyme (like “amoeba” with “ach du lieber”) or speeds up for comic effect, zinging one clever phrase after another in machine-gun-like tempo. There’s little that can follow Ms. Marcovicci’s climactic treatment of “These Foolish Things.” Most singers simply treat it as an itinerary of items that add up into a poignant statement of love and loss. Yet Ms. Marcovicci makes you feel that each entry on the list has a specific and relevant personal meaning to her, turning this classic British pop song into a kind of intimate inventory. Despite what we might think, she’s still running the show after all.

Ms. Luker’s current show takes female songwriters as its theme, and the material ranges from the jazz and pop standards of the lyricists Dorothy Fields and Carolyn Leigh up to the often very elaborate story-songs of female composers working today.

The trick with familiar chestnuts like Fields’s “The Way You Look Tonight” and Kay Swift’s “Can’t We Be Friends” is to re-animate these flexible texts with expression and originality. But performance-art pieces, like “The Noise That Joy Makes” (by Faye Greenberg, Catherine Cox, and David Evans) and “Lovely Lies” (Beth Blatt and Jeff Blumenkrantz) require a different focus. Unlike traditional musical-comedy songs, which illuminate a particular character and essentially give you a chapter of a larger narrative, most of the contemporary songs Ms. Luker does are entire stories in and of themselves – dramatic monologues set to music.

These are compelling pieces of single-actor theater, and Ms. Luker, one of the greatest Broadway leading ladies of our time, sings them movingly.The problem is that these songs rarely feature memorable melodies – and you wouldn’t want to hear Zoot Sims blowing on their chord changes.

A show consisting entirely of such songs would be too much, which is why Ms. Luker wisely alternates them with more hummable material like Betty Comden’s “Lucky To Be Me” and Carolyn Leigh’s “The Best Is Yet To Come.”

Marcovicci until June 10 (59 W. 44th Street, between Fifth and Sixth Avenues, 212-840-6800). Luker until May 20 (540 Park Avenue at 61st Street, 212-339-4095).