Riker begins the holodeck program by creating a New Orleans jazz club with an "intimate" crowd of one, and after two attempts the holodeck conjures up Minuet, a sultry brunette in a flaming red dress and sparkling diamond neckless.  Riker is entranced.  He serenades Minuet with a Glenn Miller tune on his trombone, and when they dance, Riker is amazed by how real Minuet seems -- her smell, her touch, the things she says and thinks.  When Captain Picard joins them, he is thoroughly charmed by Minuet as well.

Minuet, however, has been created by the Bynars as a lure to keep Riker on the holodeck.  The Bynars empty the ship and hijack the Enterprise to their home planet.  The aliens need the ship's computer to store the information from the planet's master computer to prevent it from being erased by and electromagnetic pulse from a nearby supernova.  After Picard and Riker discover the problem and save the Bynars' planet, Riker returns to the holodeck -- but finds that Minuet's program is gone.  He tells Picard, "She'll be difficult to forget."

That proves to be true three years later, when Riker is unwittingly captured by a young alien; Riker is put into an elaborate scenario where he believes 16 years of his life have suddenly passed and he is captain of the Enterprise.  As Riker tries to work through his memory loss, he finds out his late "wife" was Minuet, and this becomes the key to helping him realize he's in a fantasy.  Riker is told that Minuet was given this role because she was someone he had very passionate feeling toward, who in his mind "exists, physically."  Riker replies that she was "part of a very special program."