Shimmering doo-wop wafts through “A Bronx Tale,” a sinuous, accommodating sound that Chazz Palminteri frequently matches with his own street-corner symphony. His melody is notably light on the thundering dynamism that punctuates most mob tales, including the ones that have sustained Mr. Palminteri’s career for several years now. (That career was launched in 1989 when Robert De Niro saw this solo show in its original off-Broadway incarnation; Mr. De Niro adapted it into an understated and altogether lovely film in 1993, bringing its creator and star along with him.) But as the well-known character actor recreates more than a dozen of the hoods and hellions who punctuated his 1960s childhood in the titular borough, his song of himself should set more than a few toes tapping.

Except for brief interludes at City Island and a nearby black neighborhood, “A Bronx Tale,” staged unobtrusively by the veteran Broadway director Jerry Zaks, takes place no more than a few feet from the corner of East 187th Street and Belmont Avenue. Mr. Palminteri grew up in this almost exclusively Italian neighborhood, where the three syllables in “beautiful” received equal weight and kids knew both the Fifth Commandment and the Fifth Amendment by heart.

Mr. Palminteri’s robust portrayals of unsavory characters from backgrounds like this earned him an Oscar nomination (for “Bullets Over Broadway”) and several years in the upper echelons of Hollywood character actors. Ironically, his heyday as film’s go-to gangster began to recede just as the durable genre enjoyed yet another spike in popularity, this one thanks to a recently departed New Jersey crew of “The Sopranos.”

Indeed, many of the 18 characters the raspy-voiced Mr. Palminteri revisits with accomplished economy could generously be described as mezzo Sopranos, a group of scofflaws and no-accounts who hover ominously in the orbit of Sonny, a neighborhood kingpin in the making. Instead of Paulie Walnuts and Big Pussy, we get Frankie Coffeecake and JoJo the Whale. While “A Bronx Tale” begins and ends with incidents of violence, the majority of these wise guys are innocuous and entirely extraneous to the paisan’s progress of our hero.

That journey, which has been split between the narrator’s experiences at the ages of 9 and 17, involves two very different role models tugging on the impressionable young Cologio Lorenzo Romano Alfredo Palminteri. (You’d go with “Chazz,” too.) On his right shoulder — the one where the angelic alter ego sits in most cartoons — is his working-stiff father, a bus driver named Lorenzo who instills in 9-year-old Cologio an appreciation for hard work, fulfilled promise, and Joe DiMaggio. Sonny also takes an interest in Cologio’s growth, which to him starts with not wasting any time on DiMaggio or any other baseball player. (“You think Mickey Mantle cares if you live or die?”)

As the story begins, Cologio keeps his mouth shut after witnessing Sonny shoot a guy in cold blood during a dispute over a parking space. This pint-size act of omerta earns the conflicted approval of Lorenzo, who clearly fears for the boy’s safety: “You did a good thing for a bad man.” Sonny’s response is less complicated; he schools Cologio in street wisdom, gives him a flashy nickname — “C” — and lets him toss the dice at his high-stakes craps game.

Goodfellas always make for better stories than decent fellows, and it’s no surprise that Mr. Palminteri assumed the role of Sonny instead of Lorenzo when Mr. De Niro adapted “A Bronx Tale.” (The role of the stalwart dad went to a fellow who had already played his share of tough guys: Mr. De Niro.) Years later, Mr. Palminteri’s wary incarnation of Sonny — quoting “Nick Machiavelli” and banishing underlings to a local men’s room for being too fat or too unlucky — remains a high point of his often-told but nonetheless engaging story.

The second half of Mr. Palminteri’s tale takes place eight years later, as a teenage Cologio processes the lessons of these two very different men as he navigates late-1960s racial turmoil along with his own hormonal unrest. Lorenzo plays a relatively minor role in these later sequences — and one of his two scenes casts him in a jarringly unsympathetic light by modern-day standards — but his ethical counsel proves invaluable as current events tumble into Cologio’s ill-prepared lap.

Having not seen the original off-Broadway production, I’m hard-pressed to say what Mr. Zaks’s contributions might have been. The segues are handled capably enough, the pacing is more than adequate, and even if John Gromada’s music and Paul Gallo’s lighting design overembellish here and there, the physical production serves as a perfectly harmless vessel for Mr. Palminteri’s well-honed story.

And while his evocations of the very few women in his story — a weepy mother, a saintly girlfriend — are perfunctory at best, Mr. Palminteri clearly relishes breaking past the hair-trigger lunks with which Hollywood has long entrusted him. He dives with gusto into every member of the wheezing, limping, spitting, crooning crew from the old neighborhood, and his wide-eyed protagonist offers a welcome ballast to the blustering tough guys who surround him.

Engaging stories told crisply and engagingly are nothing to sneeze at. This may be a thrice-told “Tale” by now, but you know what they say about the third time.

Until February 10 (219 W. 48th St., between Broadway and Eighth Avenue, 212-239-6200).