Maybe it’s all those decades of being condescended to as the “Fabulous Invalid,” but the New York theater world has long had a soft spot for the runts of the litter, particularly those that can (sort of) carry a tune.

Two long-running series of staged musicals (City Center’s Encores! and the York Theatre’s Musicals in Mufti) pay tribute to the almosts, not-quites, and what-were-they-thinkings that have littered the Great White Way. A series of CDs hail memorable songs from “Unsung Musicals,” and a cohort of theatrical rubberneckers cherish Broadway flops with an odd blend of Schadenfreude and solicitude.

Take the composer-lyricist Jacob Sterling, whose corpus is confined largely to two stillborn musicalizations of hit movies (“Private Benjamin” and “La Femme Nikita,” the latter renamed “Mademoiselle Death”) and a handful of song cycles. The ubiquity of one of these, a slice-of-1980s-New-York collection called “What’s That Smell,” among a very select few makes it a natural title for David Pittu’s musical biography of a songwriter who “has been prominently up-and-coming for over 20 years.”

The fact that Jacob Sterling doesn’t exist is a minor detail. Tone-deaf tunesmiths are so coveted within the musical-theater community that inventing a new one from thin air makes perfect sense. It’s simply a question of supply and demand. “What’s That Smell: The Music of Jacob Sterling,” Mr. Pittu’s maniacally insular glimpse at mediocrity in all its solipsistic glory, is likely to keep those fans — though perhaps only those fans — thoroughly entertained.

One such adorer of Sterling’s oeuvre is Leonard Swagg (Peter Bartlett), who has invited the composer (Mr. Pittu, who also co-directs with Neil Pepe) to appear on his public-access television show, “Composers & Lyricists of Tomorrow.” Smut’s studio, designed with loving tackiness by Takeshi Kata, is covered with posters from underappreciated Broadway musicals such as “Greenwillow” and “Oh, Captain!” These are exactly the sorts of cult-hit flops enshrined in “[title of show],” the current Broadway musical about two aspiring songwriters. “What’s That Smell” makes “[title of show]” look like an evening at ESPN Zone capped off with a lap dance at Scores.

The songs have been composed by Randy Redd, with lyrics by Mr. Pittu; optimist that I am, I suspect that they are terrible on purpose. The score sounds at times like an anthology of “love themes” from early-’80s romantic comedies; no piano-bar cliché goes unexploited, from the echt-Sondheim arpeggios to the treacly key changes to the overexplicit lyrics. The cataclysms of the world — AIDS, September 11 — penetrate Sterling largely to the extent that they boost or impede his career. “If the word ‘hero’ or ‘survivor’ came up in a lyric, it became a 9/11 reference,” he complains. “And if I can’t use ‘hero’ or ‘survivor’ in a song, I might as well not use ‘magic’ or ‘journey.'”

Mr. Pittu, whose miniaturist drollery has buoyed recent works by everyone from Harold Pinter (“Celebration”) to Mark Twain (“Is He Dead?”), could not be more squirm-inducing as Sterling. Abetted by the reliably sharp Mr. Bartlett, here taking a rare turn as (ahem) straight man, Mr. Pittu paints a grimly hilarious portrait of a legend in his own pathologically unoriginal mind. Nowhere does this narcissism become more apparent or sharp-witted than in a ludicrous ballad that Sterling ostensibly wrote as a tribute to a former mentor:

I’ll miss him telling me I’m wonderful,

A genius, a star on the rise.

I guess the thing I’ll miss the most is myself

Reflected in Marty’s eyes.

But for every well-aimed shot at show business and its more virulent delusions, Mr. Pittu settles for an easy double entendre or tossed-off quip. Puns get a particularly heavy workout: Sterling graduates from SPASM (Southern Palo Alto School of Music) before being commissioned by CRAMPS (Cedar Rapids American Musical Performance Series), all of which has brought him to “Leonard Swagg’s CLOT” (as Swagg likes to call “Composers & Lyricists of Tomorrow”). The audience ultimately begins to parse any and every ungainly series of words well before the characters pause to spell out the abbreviation, and it all becomes a bit Laden with Acronyms of Marginal Effectiveness.

And “What’s That Smell” steadily deflates as it moves closer to the present day. The targets in an overlong new ode to brand-name shopping are unrewardingly broad, and the material here shifts from amusingly bad to, well, bad. Those fortunate enough to have had minimal contact with the Jacob Sterlings of the world might wish to keep their streak alive. But anyone with a few ghastly readings under their belt — anyone with the inclination to hug the likes of “Mademoiselle Death” close to them while hanging a “Kick Me” sign on its back — will find their nostrils flare not unpleasantly at “What’s That Smell.”

Until September 28 (330 W. 16th St., between Eighth and Ninth avenues, 212-279-4200).