Oftentimes, musical comedies thrive during the first act, when they can introduce characters and let them trill and twirl. Aaaaaand then the shows fall apart in the second act, when they have to deal with the pesky task of tying up plot strands.

With “Thoroughly Modern Millie” at Goodspeed Opera House, it’s the opposite situation. The first act starts and stalls, stalls and starts, in large part because of the time clunkily devoted to setting up the story, particularly a disconcerting subplot that I’ll detail shortly. But “Millie” finds sure footing in the second act, thanks to a wealth of exuberant, creative song-and-dance numbers.

The issue with the first act isn’t the fault of the production but rather the material. The script has some amusing one-liners, but the storyline, culled from the 1967 movie of the same name, feels its age.

Richard Morris wrote the movie (which starred Julie Andrews and Mary Tyler Moore) based on a 1956 British musical, and he co-wrote the book for the 2000 stage musical adaptation with lyricist Dick Scanlan.

Young Millie, fresh from Kansas, has come to 1922 New York City to find a husband; she plans on marrying her boss, since that’s what “a modern” would do, she theorizes. What she finds instead are — and this shouldn’t come as a spoiler alert — true love and herself.

Millie (played by Taylor Quick) is a bubbly soul who meets a cute, if financially challenged, guy named Jimmy (Dan DeLuca). Sparks fly, but Millie sticks firmly to her plan to find herself a wealthy exec to wed. She gets a job at the Sincere Trust Insurance Company, where the straight-laced Mr. Graydon rules the roost. He’s impressed by Millie’s ability to take dictation, and she’s hired.

She gets a place to stay at the Hotel Priscilla, which is overrun by young women dreaming of a career in acting.

Here’s the problematic part of things: The woman running the hotel is secretly drugging some of the young female patrons and selling them into prostitution in Hong Kong. Nothing says “musical comedy” like a subplot about human trafficking! It’s beyond jarring that that is wedged into a show that’s otherwise mostly an exercise in frivolity.

That said, the Goodspeed version handles that knotty subplot as deftly as I imagine is possible. It goes headlong for a light, breezy tone, dark subject matter be damned. Thank goodness the show has hot-ticket Loretta Ables Sayre as the evil Mrs. Meers, the Asian woman who runs the hotel and is part of the white slavery ring. She’s pretending to be an obsequious Asian stereotype, but she reveals to the audience that she is really a tough-as-nails broad who’s in control. Sayre toggles ably between those personas, mining sly humor from each. She has a strong voice, too, bringing a slightly husky tone to “They Don’t Know” and “Muqin.”

I will say that this production treats the two Chinese immigrant characters of Ching Ho and Bun Foo, who are blackmailed into helping Mrs. Meers drug and kidnap young women, in a much more respectful way than a touring version I saw a few years back. In that tour, the performances leaned uncomfortably close to caricature. Here, they’re given emotional heft. James Seol as Ching Ho and Christopher Shin as Bun Foo play them with a comic touch when needed but also with a soulfulness, especially in the scenes highlighting their internal struggle over being forced to assist Mrs. Meers in her evil mission and, on the other end of the spectrum, in the scenes showcasing Ching Ho’s shy crush on Miss Dorothy.

There’s no way to gracefully segue from talking about a sold-into-prostitution story to discussing other elements of the musical, so let’s just awkwardly jump to another subject: dancing.

“Millie” is directed and choreographed by Denis Jones, who’s currently up for a best-choreography Tony Award for “Holiday Inn, The New Irving Berlin Musical.” That show had its world premiere in 2014 at Goodspeed.

Jones does a fine job directing, but where he really shines is as a choreographer. Millie and her fellow female workers sit at their desks and let the click of their tap shoes substitute for the clack of their typewriter keys. Men wheel the women’s desks and chairs around onstage, creating swirling patterns. In a different number, Millie hits a speakeasy, and folks are draping over each other as they dance; the choreography cleverly shows the physical kick and then rubber-kneed relaxation they all get when they swig some hooch.

Another euphoric moment happens when Millie’s boss, Mr. Graydon, and Millie’s new best friend, Miss Dorothy, are instantly smitten with each other and provide the night’s most transporting number, “I’m Falling In Love With Someone.” The two performers — Edward Watts and Samantha Sturm — are absolute heaven together. Watts lets his square-jawed-handsome-composure dissolve into goofy mooning over Miss Dorothy, while Sturm’s Dorothy, with her girly-girl voice sighing, gazes adoringly with her Keane-big eyes at the object of her affection.

As for the other main romantic couple: Taylor Quick infuses Millie with youthful verve, and she sings like a dream and dances adroitly (those Charleston-style moves!). Her acting can be a little green, not quite as layered as you might hope, but she displays sweet chemistry with DeLuca as Jimmy, particularly as they croon and swoon on “I Turned the Corner.”

The score for “Millie” by Jeanine Tesori, who recently won a Tony for her work in “Fun Home,” toys with sounds of the era in an entertaining way. And it’s a pleasure to hear Ramona Keller, as renowned singer (and giver-of-excellent-advice to Millie) Muzzy, turn her power and finesse on “Only in New York” and “Long As I’m Here With You.”

The costume design by Gregory Gale reflects iconic 1920s styles (fringe, yes; flapper looks, yes). The scenic design by Paul Tate dePoo III is all art-deco cool, with savvy lighting design by Rob Denton.

The Hotel Priscilla elevator is created with the sliding elevator-cage doors and then rushes of light zipping up the side of the wall, giving the sensation that the “elevator” is moving. (All while the characters tap dance, because why wouldn’t people tap dance on an elevator? It’s a musical!)

Another eye-catching set: The exterior of the office building where Jimmy and Millie dance along the ledge is all angles and dramatic perspective. It almost feels as if they is dancing on air, just as any musical romantic should.

 k.dorsey@theday.com

If you go

What: “Thoroughly Modern Millie”

Where: Goodspeed Opera House, 6 Main St., East Haddam

When: Through July 2; 2 and 7:30 p.m. Wed., 7:30 p.m. Thurs., 8 p.m. Fri., 3 and 8 p.m. Sat., and 2 p.m. Sun.; also performances at 2 p.m. on select Thursdays and 6:30 p.m. on select Sundays

Tickets: Start at $29

Call: (860) 873-8668