Avi Steinberg’s memoir, “Running the Books,” about his job as a prison librarian at “the Bay” — the Suffolk County House of Correction in South Bay near Boston — gets off to an obnoxious start.

Mr. Steinberg is a self-described “asthmatic Jewish kid,” a young Harvard graduate and a stalled novelist. He applied for the prison library job when he saw it posted on Craigslist. He needed the health insurance. Probably he needed a book idea too.

The early bits of “Running the Books” are as hopped-up as a spaniel with a new rubber ball. The tone is, more or less, “Augusten Burroughs Goes to the Clink.” Here’s a not atypical passage: “It was official. I was now on the side of angels. The Po-Po. The Fuzz. The Heat. The Big Blue Machine.”

But a funny thing happens to “Running the Books” as it inches forward. Mr. Steinberg’s sentences start to pop out at you, at first because they’re funny and then because they’re acidly funny. The book slows down. It blossoms. Mr. Steinberg proves to be a keen observer, and a morally serious one. His memoir is wriggling and alive — as involving, and as layered, as a good coming-of-age novel.

The humor bubbles up organically. When a homophobic prisoner learns about a book called “Queer Theory: An Introduction,” he bellows in agony: “They got theories now?” Mr. Steinberg gets this advice from a prison staff member on how to comport himself: “Don’t smile. This isn’t the Gap.” He listens bemusedly to one inmate’s intricate disquisition on why pimping, he relates, is “the great male art form, the art form to which all others aspired.”

Explaining his relatively pampered Orthodox Jewish background, Mr. Steinberg reports: “My yeshiva high school’s basketball team was named not the Tigers or the Hawks, but the MCATS. As in, the Medical College Admission Test.” . . .