On Santa Catalina Island, Axel Nordstrom, Arthur Godfrey, runs a glass-bottom boat tour business, while his widowed daughter, Jennifer Nelson, Doris Day helps by donning a mermaid costume to entertain the passengers beneath the waves. A playful encounter sets the story in motion when a fishing hook catches her costume, and Bruce Templeton, Rod Taylor, reels in the lower half of her outfit, leaving her momentarily stranded and adrift. The incident leads to a chance meeting at her new workplace in Long Beach, where she has landed a public relations job at an aerospace research company, and Bruce becomes her boss of sorts as he works on a secret invention.
Bruce’s team is developing GISMO, a gravitation-control device that could be launched into orbit by the U.S. Air Force in a matter of weeks, a project that has attracted intense interest from the Soviet Union. Bruce hires Jennifer to write his biography as he presses forward with GISMO, while at his home she meets electronics technician Julius Pritter, Dom DeLuise, and Edgar Hill, Eric Fleming, a CIA agent charged with guarding the project. Julius, eager to help but secretly susceptible to pressure, starts digging for information about GISMO and photographs a cryptic note Bruce sketched while brainstorming. Those photos are promptly passed along to Julius’s handler, setting the stage for a tension-filled web of suspicion.
A Catalina trip with Bruce follows, during which a remote-controlled malfunction throws them together in a surprising fashion, landing them in a parking lot after a perilous stumble. The pair share an evening at Axel and his wife’s home, trying to understand who is watching whom and why. Back at the office, Hill arranges a tense briefing with Hill, security guard Homer Cripps, Paul Lynde, and PR executive Zack Molloy, Dick Martin, with General Wallace Bleecker looming over the GISMO program. Cripps grows suspicious of Jennifer, noting odd habits—she calls the same number daily and hangs up with the cryptic line “that’s all for now, Vladimir,” she burns documents at night, and she has a shortwave antenna at home. The innocent explanations—Jennifer’s dog Vladimir, the need to burn old papers to safeguard secrets, and her method of communication with Axel—are not known to the injectors of suspicion, and Bruce begins to doubt her.
At a party Bruce hosts to showcase GISMO, Jennifer publicly professes her love for him, and they plan to spend the night together. Yet Bruce is pulled away again by Hill, Cripps, Molloy, and Bleecker, and Jennifer overhears their conversation, sensing that she’s being suspected of espionage. Bruce defends her, insisting she isn’t clever enough to be a spy, which only fuels her resolve to prove herself. She stages a bold counter-move by pretending to be a spy herself: she arranges a misleading duel of misdirection, planning for Molloy and Bleecker to confront each other in the guest room. In the process, she binds Cripps, only to realize that Hill—unseen and dangerous—has infiltrated the scene, having planted the actual secret in her purse to smuggle the GISMO formula out of the house.
The confrontation escalates as Julius confronts Hill, who arrives with a gun and demands the formula. Jennifer and Julius team up to thwart him, and she escapes as Bruce, Cripps, Bleecker, and Molloy scramble to intervene. Hill is finally stopped when neighbor Mabel Fenimore, Alice Pearce, lands a decisive blow with a bedside lamp. The danger passes, but the night’s revelations leave Bruce and Jennifer united in their resolve. The lovers embark on a honeymoon, riding the glass-bottom boat once more, only for the device to fail again and strand them in the same Catalina parking lot, adding a final twist to their adventurous fate.
Throughout, the film balances breezy charm with a spy-thriller backbone, weaving together romance, mistaken espionage, and high-stakes technology. The interplay between the charming public face of Bruce’s project and the covert threats around GISMO creates a brisk, lighthearted mystery, anchored by strong performances from its leads and a colorful supporting cast.
