Supposedly fly-on-the-wall documentaries about performers are becoming more numerous, and this one covering a year in the life of long-time stand-up comedienne Joan Rivers does the job reasonably well. Ricki Stern and Annie Sundberg follow the indefatigable septuagenarian through gigs in clubs large and small, book signings, QVC appearances, the rehearsal and performance of an autobiographical play, a routine in a bash honoring the late George Carlin, a “Comedy Central” roast, and a stint on Donald Trump’s “Celebrity Apprentice” alongside (or more properly in rivalry with) her daughter Melissa.

What becomes clear from all this is that Rivers is as driven as she ever was, obsessed with working endlessly, on anything and everything, and pushing for jobs whatever the odds against her. In the Carlin tribute she frets over comparisons with colleagues like Jon Stewart and Gary Shandling; at a gig in Minnesota she’s confronted by a heckler who objects to a joke about Helen Keller, prompting her to defend her sharp comedic style; and after her play’s inauspicious critical reception in London, she’s reluctant to bring it to New York because she fears repeating an unhappy stage experience there years before. (What she seems to want most is to be taken seriously as an actress. Certainly it’s in her comments on that subject that she’s most emotional.)

What’s equally obvious, though, is that Rivers is incredibly self-absorbed. Despite her habit of hosting a generous Thanksgiving dinner and even taking food to shut-ins (this year, her cute grandson accompanies her), most everything seems to be about her. That’s demonstrated perhaps most brutally in her relationship with her long-time manager Billy Sammeth. She initially seems devoted to him (and vice versa), but when he disappears for long periods (the reasons unexplained, though one might guess at the cause), she ultimately fires him—by e-mail. And her concern isn’t so much about the guy, who might be ill or even dead, but about the fact that, as she repeats on several occasions, with him gone she won’t have anybody from the old days to share memories with.

Most of “A Piece of Work” is concerned with the present, but it does provide enough snippets about her career—her groundbreaking efforts as a female stand-up comic, her breakthrough on the “Tonight” show, the rift with Johnny Carson when she accepted an offer from Fox to host a competing late-night talkfest, the suicide of her husband—to remind viewers of how long she’s been around. It’s a considerable accomplishment, but in her mind also a curse—since the business is skewered toward youth, one thing she can’t offer despite all the cosmetic surgery in the world.

“Joan Rivers” doesn’t really delve very deeply into its subject—it certainly captures her eccentricities and her boundless work ethic, but the explanations it suggests behind them are pretty jejune. But if this “piece of work” is more workmanlike than revelatory, it’s an engaging portrait of a feisty lady.