Pastiche — the conscious echoing of music from a bygone era — trades on what audience members already know and how that knowledge makes them feel. In lesser hands, it can be a crutch, a pandering attempt to offer up a newly minted oldie-but-goodie. But when used with an eye toward both meeting and upending our assumptions, as in Michael John LaChiusa’s “Hello Again” and, most famously, Stephen Sondheim’s “Follies” and “Assassins,” pastiche can make sense of today by spotlighting brand-new yesterdays.

Which makes Mr. Zero, the bitter everyschlub at the center of “The Adding Machine,” such a puzzling and ultimately compelling character. In refracting Elmer Rice’s legendary 1923 foray into Expressionism through a kaleidoscope of musical references, composer Joshua Schmidt and his co-librettist, Jason Loewith, have surrounded their singularly unreflective protagonist — a slow-witted blend of Willy Loman, Walter Mitty, and Raskalnikov — with the jolting, brash sounds of an America that he neither embraces nor understands.

Instead, Zero (Joel Hatch), who finds himself replaced by the titular piece of machinery after 25 years of pencil-and-blotter drudgery, stomps and seethes to the sound of what “Assassins” described as “another national anthem.” This sound, a lurching counterpoint to the promises of serenity and prosperity, will ultimately lead him beyond obsolescence to first the gallows and then a seemingly blissful afterlife that holds little appeal — Zero maintains a Marxist (as in Groucho) refusal to be part of anywhere that would have the likes of him: “Don’t tell me you wanna stay here with a lotta lowlifes … and sinners?”

Along with director David Cromer, Messrs. Schmidt and Loewith have created the sort of aggressively austere, Brechtier-than-thou presentation that shows like “Urinetown” routinely milk for laughs. (The Kurt Weill resonances make sense: Along with “Adding Machine,” Rice is best known today for “Street Scene,” the source of a Weill opera.) But they’re not fooling around. Even when “The Adding Machine” groans under the weight of its own ambitions, the spiky arias for Zero’s fellow sufferers are leavened with those tantalizing pastiche songs that offer glimpses of seemingly unattainable simplicity. The result is a bracing corrective to the pervasive role of musical theater as a lowest-common-denominator pleasure dome.

A surge of knee-pumping gospel for the pious sinner Shrdlu (Joe Farrell), a Tin Pan Alley love ditty from a melancholy co-worker named Daisy (Amy Warren), astringent dinner-party chatter that Virgil Thompson might have written: Each of these dangles the possibility of simpler, sunnier musical fare. (Okay, maybe not the Thompson scene.) Each also includes witty reminders that such optimism is unfounded: A jailer’s keys fill in as a tambourine in the first example, the prayer grace is interrupted mid-song by Zero’s shrewish wife (Cyrilla Baer), and the fragmented party talk is united only when the couples spit out their anger at “so many agitators! / All the damn foreigners!”

This xenophobic chorus, one of many platforms to show off Keith Parham’s outstanding lighting design, also marks a rare case of Zero joining in on the music; even when Zero is in these scenes, he tends to stand outside of the score. The noted exception to this comes in his anti-apologia, a courtroom aria in which he both deflects and seeks blame for killing his boss, while drifting into memories of past perceived outrages. Here and throughout, the relentlessly honest Mr. Hatch stays at a respectable distance from conventionally pleasant tones, but he successfully conveys the hangdog dignity of an eternal have-not. And he is capably matched by Ms. Baer, who lends a plush soprano to her harangues, and the charming Ms. Warren.

In addition to the aforementioned filigrees of musical wit, Mr. Cromer has imposed a structural discipline that suits Rice’s ruthlessly efficient milieu, eliding scenes and discarding several supporting characters. Each scene in “The Adding Machine” has a recognizable pulse, and Zero’s befuddled obstinance leads to a finale that sacrifices none of Rice’s didactic determinism. (Let’s just say Mr. Schmidt had quite a few more musical periods from which to draw.)

I wish the synthesizer-heavy score had sounded a bit fuller, and the outright user-unfriendliness of some of the gnarlier choral sequences can be a bit of a trial. But as the adding machines and other exemplars of modernity press forward, leaving crumpled-up artisans in their wake, the defiantly retrograde — and occasionally heavenly — medium of musical-theater craftsmanship remains in unapologetically grown-up hands.

Open run (Minetta Lane Theatre, 18 Minetta Lane, between Bleecker and West 3rd streets, 212-307-4100).