Jennifer Nelson (Doris Day) works at an aerospace lab, but moonlights as a mermaid to boost sales for her father's glass-bottom boat company. When her coworker, Bruce Templeton (Rod Taylor), accidentally hooks her costume while fishing, he is smitten. Back at work, Bruce brings her in as his biographer -- a pretense for wooing her. Meanwhile, inept security agents Julius Pritter (Dom DeLuise) and Homer Cripps (Paul Lynde) wrongfully peg Jennifer as a Soviet spy, causing all sorts of problems.