<i> One More Time:</i> A MEMOIR by Carol Burnett (Random House: $18.95; 359 pp., illustrated)

There are any number of ways to be touched by a book, but it usually begins through one set of artifices or another, made up out of imagery, style, suspense, evocativeness and a compelling vision that together form an accumulation of moments such as poet Marianne Moore has described, as “lit with a piercing glimpse into the heart of things.”

Carol Burnett’s memoir (the word stands here in subtle distinction from “autobiography”--more on this in a moment) contains none of these elements in abundance, but it’s moving just the same as an expression of a gentle, affectionate woman who endured a considerable amount of childhood pain and looks back on it now without rancor or self-pity.

“One More Time” is not a literary work; it was never intended to be. It began instead as a letter to her three daughters about the portion of their mother’s life they could never have witnessed. “I wanted to go through it all, one more time,” she writes, “to let you in on my growing pains, dreams, goofs and what-have-yous, so that maybe you could figure out, in case you’d ever want to, just how your mom turned out to be the kind of hairpin she is . . . and more than anything, I wanted you to know Nanny and Mama and Daddy, since there’s no other way now.”

Though the story ends in the present, “One More Time” is essentially about childhood and family. The Burnett family came from San Antonio. Her parents moved to Santa Monica when she was 4, but shipped her home when their marriage began to unravel. When the family fortunes in Texas took a severe downturn, her grandmother brought her back to Hollywood, where both of them would live with--over her strenuous objections--Carol’s mother Louise (they all for a time drew on welfare).

Mabel Eudora--”Nanny”--was suspicious, moralistic, sarcastic, manipulative and a bit of a liar and hypocrite (she had more marriages and affairs than she would admit to, which didn’t stop her condemning Louise, who grew up misinformed about the identity of her real father). She wore false teeth and long johns with a drop seat, and never made their Murphy bed; she was flatulent. Carol idolized her.

She in turn held Carol so close that occasionally she’d write a note excusing her from school so they could spend the day together. Nanny is the most vivid character in the book, and even when unpleasant truths about her emerge, she’s never treated with opprobrium. She was too eccentric and too much fun.

Louise and Jody (Carol’s father) are, respectively, less well seen because both lived at some remove, Louise steadily withdrawing into her own disappointments and alcoholism (she lived down the hall from Nanny); Jody, also an alcoholic (which often made him persona non grata ), into dispiritedness and illness.

Both of them were too fragile for the world’s rough demands. Louise is recalled as a beautiful, romantically inclined woman with a singing talent who didn’t have the cleverness or the drive to push for a career, and whose looks and health were destroyed by booze. She endured with equanimity both poverty and the shame of bearing Carol’s half-sister Chrissie out of wedlock (Carol regards this as a heroic act, considering the time and Nanny’s relentless vituperations).

Jody’s drunkenness enraged Carol as a child (she felt betrayed by his promises to give up drinking), but one of the most heart-rending passages in the book deals with her visit to Jody in a tuberculosis ward. His life is dead-ended; she’s en route to a career in New York, a place that to Jody is as distant as Mars. His pride in her is inarticulate, but unmistakable. The passage is written sparsely, with little adjectival coloring. But in it, you sense Carol’s rediscovery of him in writing, and how much she loved him.

“One More Time” contains numerous anecdotes about girlhood, including descriptions of school life and the kids on the block, and it matter-of-factly traces her self-discovery as a performer at UCLA. (It was, paradoxically, in front of an audience that she felt most hidden.) Her struggles in New York are also somewhat dryly related, as is her rise to prominence, roughly beginning with a nightclub song called “I Made a Fool of Myself Over John Foster Dulles” and her success on the Garry Moore show. She does not appear to share her mother’s romantic feelings about men she has loved (even if Louise only loved one man). Her first husband, Don Saroyan, seems more a chum than a mate (though their early career struggles kept them apart). Second husband Joe Hamilton isn’t mentioned.

The book is otherwise redeemed by its effort at honest recall. This isn’t a celebrity bio whose author has found a new milieu in which to perform a star turn. The spirit of its ending is very much like the ending of one of Burnett’s variety TV shows, when she comes out to say good night, and you momentarily sense that you’re not just looking at an entertainer--you’re looking into the face of a human being.