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At the urging of radio gossip broadcaster Tommy Keenan, oil heiress Joan Winfield and band leader Allen Brice decide to elope to Las Vegas.  Keenan charters an airplane for the trip from pilot Steve Collins, whose only plane is about to be repossessed by a finance company.  Steve is something of a ladies' man but misrepresents himself as a married man and the father of two children in order to remain unattached until he can afford to purchase a fleet of planes.

When Joan's father, Lucius K. Winfield, learns of his daughter's pending marriage from Tommy's broadcast, he telephones the airfield to stop the flight.  Steve offers to deliver Joan, unwed, to Amarillo, Texas—as far as he can fly without refueling—for ten dollars per pound of her weight, a sum that will enable him to pay his debt.  Through a ruse, Steve causes Allen and Tommy to leave the plane and takes off with Joan, explaining to her that she is being kidnapped.  Joan offers Steve twice the ransom he is asking if he will take her back to Los Angeles.  When he refuses, she attempts to parachute from the plane, but Steve keeps her inside by banking the plane sharply.

In the process, the plane is damaged and Steve is forced to land in the desert.  Meanwhile, Tommy and Allen board a plane for Amarillo, hoping to intercept Steve and Joan.  After spending the night in the desert, Joan spots a town on the horizon and she and Steve investigate.  At first, they believe the town of Bonanza is uninhabited, but when they see a plume of smoke, and follow it, they find lone resident Pop Tolliver waiting to cook them breakfast.  After Joan signals a search plane, Allen and Lucius rush separately to retrieve her.  Unaware of the new developments, Steve locks Joan in the town jail until he can fix his plane.  She escapes and, followed closely by Steve, heads for an abandoned mine shaft, where she causes a cave-in that traps them inside.

Leaving Joan behind, Steve searches for an escape route and winds up back at Pop's.  Pop convinces Steve to keep Joan in the mine until Lucius arrives, but his plans are thwarted when, after Steve admits he is not married and has fallen in love with Joan, she learns that he knows a way out and demands that he free her from the mine.  Then Allen and Tommy arrive with a Nevada judge and a flock of reporters.

Unknown to them, Bonanza is actually in California, and realizing that this would nullify any marriage performed by a Nevada judge, Steve suggests they perform the marriage ceremony there.  Lucius' plane is heard overhead and just when it looks as if everything will work out for Steve, Joan and Allen fly off for Los Angeles.  When Joan realizes that her marriage is not legal, however, she happily parachutes out of the plane and lands on a cactus.  Her anguished screams bring Steve and Lucius running.  Later, Joan and Steve wed and honeymoon with Lucius and Pop in Bonanza.