On the fourth anniversary of his wife's death, Sisko takes a melancholy late-night stroll along the Promenade, where a lovely alien woman named Fenna engages him in conversation. Strangely, however, Fenna disappears almost as quickly as she appeared. The next day, Sisko and Dax meet with Professor Seyetik, an expert in bringing dead planets back to life, who has come to re-ignite the dead sun of solar system Epsilon 119. Sisko and Dax discuss the upcoming mission over dinner, but Dax notices that Sisko is strangely distracted. Once the meal is over, he wanders back to the spot where he met Fenna, and is delighted when she suddenly reappears. They make plans for a picnic the next day, but when he asks her to tell him about herself, she runs away without warning.
Sisko asks Odo to look for Fenna, and is then approached by Dax, who questions him about the woman she saw him with the previous evening. Since he knows almost nothing, there isn't much to tell. That night, he, Dax and the rest of the senior staff join Seyetik on the science vessel Prometheus for dinner, where the professor bores them all with endless accounts of his intellectual escapades. Finally, he introduces his wife, Nidell — and Sisko and Dax are shocked that the woman looks exactly like Fenna. Strangely, she doesn't seem to recognize Sisko at all.
After the meal, Sisko tells Dax that he is almost certain the shy Nidell is the same outgoing Fenna he met on the Promenade the day before. He casually mentions the meeting to Nidell, but she claims to have never seen Sisko before. However, she is visibly disturbed when he mentions the name Fenna. Back on Deep Space Nine, Sisko tells Odo to call off the search for Fenna since he found her on the Prometheus. Odo replies that this is impossible since no one but Seyetik has been off the vessel since it docked at the station. Frustrated, Sisko heads back to his quarters and finds Fenna waiting for him. When he tells her about Nidell, she obviously has no idea what he is talking about. Sisko continues to press Fenna, asking where she came from, and she tells him that she came to the station to find him. Fenna kisses him passionately, but after he returns the kiss, she disappears — right before his eyes.
While Dax prepares for her mission with Seyetik, Sisko announces that he is coming along, hoping this will help him unravel the Fenna mystery. Soon, the Prometheus is headed toward Epsilon 119, with Seyetik prattling on in his usual fashion. He finally tells the story of how he met Nidell when he brought her planet, New Halana, back to life. Hoping this is a clue, Sisko visits Nidell in her quarters, but she says she is too sick to see him. Sisko returns to his guest quarters, where Fenna is waiting for him. Immediately, Sisko summons Dax, who scans her with a tricorder and announces that Fenna is made of pure energy. Sisko then leads Fenna back to Seyetik's quarters where Nidell is on the floor, unconscious. A panicked Seyetik begs him to help, and much to Sisko's surprise, recognizes Fenna.
Seyetik explains that Nidell is a psychoprojective telepath and that Fenna is just one of many images she has created. Sisko asks Seyetik why this is killing her, and the professor explains that Halanans lose control of this ability while under stress. He sadly admits that he is probably the cause of that stress, but adds that since Halanans mate for life, Nidell can never leave him. When Fenna realizes she truly has no past to tell Sisko about, it becomes clear that Seyetik's story is true. Realizing that their love is only a dream, Fenna kisses Sisko goodbye and prepares to return to Nidell to save her life. At that moment, Dax summons Sisko to the Bridge — Seyetik has taken a shuttlepod and is heading toward the dead sun. Realizing the professor means to kill himself, Sisko tries to stop him, but Seyetik insists that he wants to set Nidell free. His ship explodes on impact, the sun is brought back to life, and Fenna slowly disappears. Back on Deep Space Nine, Nidell recovers, but because she cannot remember her "life" as Fenna, her feelings for him are gone. She leaves the station to return to New Halana, and Sisko is left to cope with the pain of another lost love.