Stardate 1329.1: The Enterprise is pursuing a vessel which they soon identify as a cargo vessel. The pilot is overloading his engines and refuses to respond to hails. The ship enters an asteroid belt then loses its engines. Kirk orders them to put a deflector shield around the ship to protect it despite the drain on the shields. Spock and Scotty go to the transporter room with McCoy to beam aboard the cargo ship's crew as the lithium crystals start burning out. The captain of the cargo ship finally sends a signal and they lock on and beam him over. The captain is a roguishly dressed figure who demands to know who they are and identifies himself as Leo Walsh and says he has three more crew who are ready to beam over. Scotty locks on just as the ship is destroyed by an asteroid. Scotty manages to bring them over and they resolve as three beautiful women.
Kirk gets the Enterprise out of the asteroid belt while McCoy, Scotty, and even Spock are bemused by the incredible beauty of the women. Kirk demands to see Walsh in his quarters and Spock escorts Walsh and the ladies through the ship, drawing the attention of every male. Kirk is equally taken back when they arrive and Walsh explains that the women are his cargo: The women are taken out and Walsh protests that he didn't know who was pursuing him. Kirk convenes a ship's hearing and isn't impressed with Walsh's blustering.
Scotty warns Spock that they have only one lithium crystal remaining, while it becomes clear that the women are having a hypnotic effect on the crew. Walsh meets with the women and he tells them not to lie, but not to submit to a medical exam. They also refer to him as "Harry," which he cautions them not to do.
With the backup circuits burned out, Spock suggests they go to Rigel 12 where there's a mining outpost. They set course for Rigel 12 and Kirk calls the hearing. The computer easily determines that "Walsh" is lying and he is forced to admit he's Harcourt Fenton Mudd, with a considerable criminal record, He claims Leo Walsh passed away and he took his name, but the crew are more interested in the women. Mudd reveals he was taking the three women to act as wives for settlers. Eve defends their choice, saying they want better lives. Kirk closes the hearing and orders Mudd to be handed over to the legal authorities. Eve demands to know what will happen to them and the last crystal burns out, leaving the life support on batteries. Mudd, realizing what's happening, tells the women that they can now have rich lithium miners as husbands, and he'll be rich enough to command the Enterprise.
While Mudd is confined to his quarters, the women have free access to the ship. One of them, Ruth, goes to Sickbay where her presence sets off the monitors. She determines that the miners are in good health. The third, Magda, gets access to a communicator from Farrell. Eve ends up in Kirk's quarters saying she sought refuge in his quarters against all the male crew staring at her. She comes on to him at first, but then says she can't go through with it, and she hates the whole thing. She storms out and goes to Mudd's quarters where Ruth and Magda are reporting with what they've found out. Eve comes in, looking the worse for wear and saying it must be near the time.
Kirk is getting frustrated with the distracted crew and McCoy reveals Eve refused a medical scan. The captain wonders if the women are alien illusions but McCoy doesn't think so. Meanwhile, Mudd uses the stolen communicator to contact the miners from quarters.
The Enterprise arrives in orbit about Rigel 12 with three days left and prepares beams the miners Ben Childress and Herm Gossett aboard. Meanwhile, Mudd is searching through his quarters for pills while the women are turning wrinkled and aged. Mudd finally locates the pills and Ruth and Magda take them immediately and revert to their beautiful selves. Eve is hesitant but Mudd reassures her and she reluctantly takes them.
Childress arrives to meet with Kirk and informs him that they'll swap the lithium for the women, and Mudd goes free. Kirk refuses and points out that the miners will have trouble surviving without Federation support. Childress considers what he says… but Mudd arrives with the women and the miners quickly stand by their proposal.
Kirk and Spock beam down with Mudd to give in and collect the crystals, but the three miners are preoccupied with the women and tell him to wait. Rigel 12 is a barren planet with dust storms and they have no choice but to wait. Childress tries to get closer to Eve but she is faltering again so he cuts in on Gossett, who tries to cut in on the third miner. A fight breaks out and Eve runs out into the storm. Kirk goes after her, telling Childress to have the crystals when he gets back. Childress goes out as well. Unable to find her, he beams back to the ship to conduct scans but the magnetic storms are ionizing the atmosphere. They have only five hours of power left and are having difficulty contacting the miners.
Childress finds Eve and brings her to his personal quarters. With 43 minutes left, they detect heat readings from Childress' quarters. Kirk has Mudd beam down with him. Meanwhile, Eve is cooking Childress a meal and cleaning up his quarters. Childress is impressed despite himself and takes her advice on cleaning his pots and pans. He comes back to find her plain looking and not particularly appealing. He starts to snap at her when Kirk and Mudd arrive. The captain forces Mudd to explain that he's been giving the women an illegal Venus Drug, which enhances people. The other miners have gotten married over subspace radio but it's a fraud and they can get out of it if they want. Childress is angry but Eve snaps at him and takes the drug, becoming beautiful again while saying it isn't real. She asks him what he really wants: a wife or a trophy. However, Kirk reveals the drug was a fake that they substituted. Kirk demands the lithium crystals and Childress gives them up. He asks Eve to stay at least long enough to talk, and she agrees, realizing Kirk has a woman of his own: the Enterprise. Kirk takes Mudd along with him despite Harry's suggestion he leave him behind. Back on the ship, the power is restored and Spock is glad that the whole emotional incident is over.