Maggie Smith was new to many American cinema audiences when she won an Oscar for her role in 1969's The Prime of Miss Jean Brodie, but these days she's got one of the best-known faces on the big screen—and the small one, where she'll pick up her fan-favorite Downton Abbey role, as the Dowager Countess of Grantham, when the show returns for U.S. viewers on Jan. 4.
With Jean Brodie fresh in readers' minds and Smith appearing with her then-husband Robert Stephens in a Los Angeles production of the play Design for Living, LIFE Magazine sent a reporter to profile Smith and Stephens. And, it turned out, much of the story focused on that now-famous face. "Maggie Smith, 36, had grown up believing she was ugly, and could only succeed as a comedienne. In fact, her distinctive face and style made her a natural scene-stealer in her early movies (The VIPs, Young Cassidy), which paved the way for greater triumphs," the July 16, 1971, story read.
In the interview, Smith confesses that she still feels that her looks are unusual for a film star, and that the make-up crew always fusses a little too much about her under-eye bags, but that she's old enough and successful enough for it not to matter. And, in saying so, she demonstrates that the Dowager Countess isn't the only one who has a way with a witty rejoinder: "Some aphorist once said that nobody has the right to be shy over the age of 25—and that applies to me."
Plus, points out Stephens, she's not the only actress to find success despite her own insecurities about her face. Shirley MacLaine, for example, he says, "has always been worried about her eyes being too small and too close together"—and that didn't hold her back. In fact, she's still going strong. Case in point: She's frequently guest-starred on Downton Abbey, opposite Maggie Smith.
Liz Ronk, who edited this gallery, is the Photo Editor for LIFE.com. Follow her on Twitter at @LizabethRonk.