Designing costumes for a period piece can be a difficult task. The additional challenge of dressing a Hollywood starlet doesn’t make it any easier. But Isaac Mizrahi has shown surprising restraint in letting Amanda Peet look a bit unkempt in “Barefoot in the Park.”

The temptation in designing clothes for a star is to make her stand out. In the recent film “Walk the Line,” for example, Reese Witherspoon was at her most beautiful, but she didn’t look like June Carter Cash. Onstage, casts are often dressed in the Broadway vernacular instead of the time period of the play. One short-lived musical, “Good Vibrations,” dealt with the problem of updating 1960s fashions by keeping the female cast in bikinis throughout most of the production.

Mr. Mizrahi’s ability to bring his name to the show without making his clothes speak louder than their context is admirable – especially from a man who has been known more for his personality than high fashions in recent memory. He is currently starring in his own television show on the Style network, and when he’s not grabbing starlets’ breasts on the red carpet while giving fashion commentary, he has branded his name in a line of low-cost clothing at Target.

In “Barefoot in the Park,” Mr. Mizrahi has not only pegged the era; he’s also created fashions that are both iconic and – most important – believable. His designs for Patrick Wilson seem appropriate to a young lawyer, while Tony Roberts’s clothes look like they came straight from a thrift store; the designs for Jill Clayburgh are lush and beautifully fitted. Ms. Peet’s Corie Bratter looks like a young newlywed of the 1960s, not a woman who spontaneously purchased all of her clothing in the fall of 1964, or what a 21st-century woman would look like if she wore retro fashions. She may own cute dresses, but they don’t always fit perfectly. Her outfits don’t always match, and her presentableness has more to do with her innate beauty than the swank clothing she’s been put in.

On Ms. Peet’s svelte frame, Mr. Mizrahi has allowed himself to do something most designers can’t bear: He’s let his clothes be unsexy. While clunky designs could be the product of a lazy, or inept, designer, the fashion choices Mr. Mizrahi has made are all deliberate. He has said: “My goal here was not to design costumes, but to almost document what the winter of 1965 was like. I wanted this to be as random as real life.” And Mr. Mizrahi lets the audience see it all, from Corie’s slightly embarrassing and dowdy undergarments to the tragi-comic exposed zipper on the back of her pants.

Ms. Peet’s costumes, in short, come off as refreshingly dull. It’s just what the staging called for.