Some plays look the same in every production — some musicals, too. The original designs for shows like “Sweeney Todd” or “Equus” or “Waiting for Godot” seem inevitable to the point that it takes an act of God (or a rebel angel) to create a fresh look. But within an unchanging shell, real actors always find ways to adapt.

Historically, productions of “Mother Courage” have taken minimal liberties. Where’s the room to maneuver? All that keeps the play going, after all, is the movement of offstage armies across the war-torn map of 17th-century Europe. Onstage, Mother Courage tags along, hawking whatever wares she can get her mitts on, jawing politics, and doing her level best to hold together her dwindling family. Give the woman a covered wagon and a rickety turntable to pull it on — and presto! She’s on her way.

Does George C. Wolfe’s new “Mother Courage” for Shakespeare in the Park have the turntable? Check, right where it has to be. And the wagon? Check — hidden at first, more or less, by a wooden fence. Then the house lights go down and next thing you know, the fence parts like the Red Sea. Meryl Streep barrels in, all set to spar with the border guards and make a buck on a buckle or a brandy or a bag of bootleg ammo, honking out a new tune by composer Jeanine Tesori with the Weimar pizzazz of a second Ute Lemper.

No, this is not your granny’s Mother Courage. I know — because my first Mother Courage was the first Mother Courage of them all, though not on her first round. She was Therese Giehse, born Therese Gift in Munich in 1898. By the time I saw her, she was into her 60s. Her acting, it was said, was much admired by Hitler. Not returning the compliment, she emigrated to Switzerland in 1933.

Bertolt Brecht was a fan of Giehse’s, too, but “Mother Courage” was not written with her in mind. (Two roles that were — both by the Swiss playwright Friedrich Dürrenmatt — are Claire Zachanassian, the vengeful plutocrat of “The Visit,” and Mathilde von Zahnd, in “The Physicists,” a lunatic psychiatrist who holds the nuclear apocalypse in her hand.)

Brecht and his wife Helene Weigel, also an actress, had fled to Sweden from Germany in 1939. Shortly after his arrival, the German invasion of Poland prompted “Mother Courage and Her Children,” his scathing though ambiguous indictment of war. Banking on a premiere in Stockholm, he wrote the title role for Naima Wifstrand, a Swede, and dreamed up a mute part for Weigel as Mother Courage’s softhearted daughter Kattrin. But the play was too explosive for Scandinavia in those precarious days. The premiere took place two years later, in Zurich, Switzerland, with Giehse in the title role. Brecht saw no more of her performance than he could glean from the reviews. In future years, he would assert that the role had been written for Weigel, and the production he mounted for her in Berlin in 1949 became the model to which all future stagings referred.

All except the revivals with Giehse. How many of them there were, I don’t know, but Giehse was still riding that wagon when a starstruck little boy from Schenectady, New York, first saw the play in Zurich, his new home. In the lobby, disapproving Swiss informed my mother that I was too young to be there, and they were probably right. Happily for me, she ignored them, and not for the first time. A lot went over my head. I had no clue what was going on when soldiers bore the bullet-riddled corpse of Swiss Cheese onstage and Courage shook her head — eyes averted, chin in the air — denying that she knew him. But like much else in Giehse’s portrayal — the casting of lots, the haggling, the iron hand she showed when her growing boys get itchy — it left an impression still legible decades later.

Giehse was not a pretty woman. Someone once said she was “built like a dumpling with the eyes of a basset hound.” Physical charm? She had none. Her speech was gruff, matter-of-fact, with no tears for spilt milk. The world was what it was; she saw what she saw, she took her best shot, and she moved on. Another character calls Mother Courage “a hyena of the battlefield,” a preposterous charge Brecht supposedly meant to stick. She looks out for number one, yes, but as a profiteer, she scarcely exists. Deep down, Mother Courage has a lot in common with Tevye the Milkman in “Fiddler on the Roof.” Like him, she’s a mother hen helpless to protect the brood.

It could not have been said of Giehse, as an approving Brecht said of Weigel, that “her way of playing Mother Courage was hard and angry; that is, her Mother Courage was not angry; she herself, the actress, was angry” — angry at the stupidity of the character she was playing. How, one wonders, could an audience tease out such elaborate dislocations? But Brecht’s play has more facets than his propaganda. For one thing, there is the matter of sex and romance. Beneath her bullish, mannish nom de guerre, Mother Courage is Anna Fierling, a woman who has known the three fathers of her children and other lovers, as well. The implication is strong that she has been raped once or more — a fate she imagines to be reserved for scrubbed, pretty girls. To keep Kattrin from harm, she rubs her face with ashes. It doesn’t work.

Giehse left Anna Fierling’s power over men unexplored; Ms. Streep revels in it. That is not the only vector on the first Courage and the latest one differ. Against memories of Giehse’s gyroscopic steadiness and cunning, Ms. Streep’s fluttery, neurotic chatterbox comes off at times like a Diane Keaton take on Eliza Doolittle. American actors these days, even the best of them, seem to think they’re falling down on the job unless the show a little shtick. (Playwrights have begun to factor that in. The high moral purpose of John Patrick Shanley’s “Doubt” did not exclude its comic moments, and Cherry Jones’s Sister Aloysius pounced on every one — very unlike Dominique Labourier in Roman Polanski’s Paris production, whose hot tears seemed wrung from a stone.)

Ms. Streep has her most original yet most artless moment late in the play, with Anna’s lullaby for her murdered daughter. At the same point, Giehse dropped her guard for once, intimate and tender as never before. Ms. Streep’s song to the same text is public as well as private; a requiem for one fallen child that implies a requiem for all the fallen children and all the other fallen besides. When I first saw “Mother Courage,” there was no war on that I knew of. Now there is, and the play radiates to every corner of the earth.