John Emmett is on a fishing vacation that will eventually take him to Texas to visit his family when his car breaks down. After he sells the vehicle to a tow truck operator, John accepts a ride from Ann Nicholson, who is anxious to reach Santa Fe, New Mexico and asks John to share the driving with her. At midnight, John stops for coffee and is approached by nurse Helen Bethke, who has been following them and tells John that Ann has had a nervous breakdown and is in the care of a Dr. Frederick Simmons. Helen asks John to contact her once they reach Santa Fe. The next morning, John and Ann are pulled over by officers in a police patrol car who state that Ann is wanted for questioning in a murder investigation in Los Angeles. Although John and Ann are handcuffed by the officers, they manage to outwit them, take the keys to the officers' patrol car and drive off. After John demands an explanation, Ann recalls how she has come to this point: Three months earlier, Ann, a former German citizen, discovered that her brother Kurt was a prisoner in East Germany. She flew to Berlin and learned from an escapee named Karl Plesser that Kurt had been working with Dr. Reinhardt Kissel, an old family friend. Kissell, an intercontinental guided missile expert who had been forced to work for the Russians, escaped and was now safe in America. Karl then tells Ann that Kurt was killed when he and Kurt tried to escape. Kissel had previously asked Kurt to take his Russian research documents, encoded as scratches on a steel mirror, with him. Karl then hands the mirror to Ann and asks her to deliver it to Kissel. When Karl leaves, he is shot and killed by a Soviet agent. Ann explains that since returning to Los Angeles in shock, she has been treated by Dr. Simmons. She tried to locate Kissel and consulted the CIA, which said it would send an agent to interview her. However, when Ann saw a newspaper report stating that Kissel had been appointed to the faculty of a university in Santa Fe, she decided to go there. John and Ann drive on and after stopping at a motel, John discovers that the handcuff key is among the keys he took from the patrol car. After removing the handcuffs, they see a newspaper story about a CIA agent found shot to death in Los Angeles. Although Ann tells John that she was not involved, he no longer knows what to believe. In Santa Fe, they go to the home of Dean William Brant, the university official who had announced Kissel’s appointment, and show him the clipping, but Brant denies any knowledge of Kissel. When Ann becomes distraught, John hands her over to Simmons, who plans to commit her to a nearby sanitorium for mental patients. John senses something is not right with the situation and checks into a nearby fishing lodge where he is approached by Kirk Kirkpatrick, a CIA agent who listens to his story, then tells him that Kissel is working in a government test center nearby. After Ann escapes from Simmons and rejoins John, they realize that they are in love and decide to marry immediately. Meanwhile Simmons and Brant, both Soviet operatives, order a gunman to find John and Ann and kill them, but they have headed to the Numa Test Center where they meet Kirkpatrick, who takes them to see Kissel. When Ann meets Kissel, she realizes that he is an imposter and hands him a lipstick she says contains microfilm, instead of the steel mirror. After Kissel leaves, Ann tells Kirkpatrick that the man is an imposter and gives the mirror to Kirkpatrick, who then asks her and John to help him entrap Simmons and Brant. As John and Ann leave their hotel, Simmons shoots at them but is shot by an FBI agent. John and Ann are unharmed and Brant is captured soon after while trying to escape. Later, Kirkpatrick reveals that the FBI planted the newspaper article about Kissel’s university appointment in order to draw Ann to Santa Fe. John and Ann spend their honeymoon fishing.