The Enterprise docks at Starbase 74 for a computer refit and some much-needed rest. The maintenance crew, four Bynars (beings who have lived with computers so long that their thinking is virtually binary), seem a bit ill at ease, but there is no apparent threat. Picard goes off-shift, and Riker takes a stroll around the ship, leaving Wesley the bridge.

Riker eventually goes to examine the Bynar- enhanced holodeck, programming it for a jazz bar in 1958 New Orleans. After playing the trombone for a little while, he quickly starts romancing the woman in the bar, named Minuet. Picard walks in a bit later, and Minuet immediately greets him in French and invites him to stay.

Suddenly, Wes alerts Data, who's in his quarters, saying there seems to be a problem with antimatter containment. Data and Geordi rush to Engineering, where their fears are confirmed: antimatter containment is about to collapse. Data immediately orders evacuation, and everyone leaves, except for Picard and Riker, who, mysteriously, don't hear the alert.

After everyone else reaches the starbase, the containment inexplicably regenerates, as the ship warps away. As the crew on the starbase try to figure out a way to recover the Enterprise, Picard and Riker finally realize that Minuet's trying to keep them in the holodeck, and leave, where they discover what's happened. Not willing to let the ship fall into hostile hands, they first set the auto-destruct, then beam intraship to the bridge, where they find the Bynars unconscious, dying, and asking for help.

The ship reaches Bynarus, the Bynars' planet, which is also dead. Picard and Riker return to the holodeck and query Minuet about what has happened. Apparently, a star in the Bynarus system went supernova, and the electromagnetic pulse knocked out the planet's central computer. The Enterprise was needed to store the data from the planet during the shutdown time. Picard and Riker, working together, manage to get into the Bynarus file and reboot the computer. The Bynars revive and are taken into custody. When questioned, they say they didn't ask because "you might have/said no." The ship returns intact to the starbase, but Riker finds that Minuet, whom he was falling for, was a Bynar creation and is now lost forever.