Kiss Me Kate, the musical comedy about a troubled production of The Taming of the Shrew in post-World War II Baltimore, doesn’t lose much sleep over the misogyny inherent in the play that inspired it. Conditions have improved more for women in the 66 years since Kiss Me Kate won the first Tony Award for Best Musical in 1949 than in the three-and-a-half centuries dividing that milestone from the early 1590s, when the Bard of Avon wrote his hilarious romp about a young gentleman of Verona who engages in a campaign of starvation, sleep deprivation, and psychological warfare to make his headstrong new bride docile and subservient. The poster for MGM’s 1953 film version of Kiss Me Kate showed Howard Keel (as Petruchio, the gentleman) putting Kathryn Grayson (playing Katherine, his non-consenting spouse) over his knee to deliver what must be the most famous spanking in two-and-a-half millennia of theater.

While Bella and Samuel Spewack’s script for Kiss Me Kate incorporates many of Shrew’s most famous scenes, its backstage plot owes as much to the remarriage-themed comedy films of the 1930s and ’40s—The Awful Truth, The Philadelphia Story, His Girl Friday, and The Lady Eve, to cite a few of the very best—as to Shakespeare. Fred, the producer/director of the show-within-the-show, is playing Petruchio opposite Lilli Vanessi, his about-to-remarry ex-wife, as Kate. Each is still in love with the other, but too proud to admit it. Meanwhile, a reprobate gambler in the cast—also the boyfriend of the young actress with whom Fred has been enjoying a therapeutic dalliance—has signed Fred’s name to an IOU held by a Baltimore gangster. When the gangster sends a pair of legbreakers to collect, Fred drafts them into the show.

It’s a fun, comic premise, but Cole Porter’s songs are why the show is remembered and revived. (The Shakespeare Theatre Company’s new Kate will open in November, with an all-male, “gender-blurred” Shrew to follow in May.) The Herndon-based NextStop Theatre Company’s game new production with a cast of 11 (plus a four-piece orchestra directed by pianist Steve Przybylski) feels a little cramped—the company and its ancestor, the Elden Street Players, have operated out of their cozy black box space in a strip mall for more than 25 years—but it’s enjoyable nonetheless. It’s longer on spit than it is on polish, but that’s not much of a problem in a show about a striving theatre company. Paul Scanlan is likably harried as the beleaguered Fred/Petruchio, and slightly more at ease with the material than his fellows. Karen Vincent, as Lilli/Kate, more than matches him as a singer, though, making her mark early with “So in Love,” one of the show’s most enduring numbers.

Another one, “Too Darn Hot”—a sterling example of Porter’s ability to sail a song about sex past the censors—gets a sultry reading from Hasani Allen and Daphne Epps. The song then blossoms in a full-cast (minus Fred and Lilli) number, and the show’s best showcase for choreographer Rachel Dolan’s trick of finding a way for nine people to dance in a space as compact as this one. Ultimately, the show isn’t reduced by its paucity of stage space nearly as much as it is by the building’s paucity of toilets—a limitation that extends intermission to a momentum-sapping half-hour, which only makes the narrative wheel-spinning in the show’s second act stick out more.

Of course, that halt in the action permits a few more classic tunes. Emily Levey brings the right amount of flirtation to “Always True to You (In My Fashion),” and Kevin Place and Drew Stairs’ awkward singing and dancing doesn’t diminish the pleasure of “Brush Up Your Shakespeare” in the least. Assessing the original Broadway production for the Dec. 31, 1948 New York Times, critic Brooks Atkinson observed that the song, which advises men to memorize a few sonnets to aid in seduction, was “fresh out of the honky-tonks” before remarking of Porter, “All his lyrics are literate, and as usual some of them would shock the editorial staff of The Police Gazette.” Yesterday’s salacious outrage is today’s Great American Songbook.

269 Sunset Park Drive, Herndon. $40. (703) 481-5930. nextstoptheatre.org.