Ben Reich is the impetuous owner of Monarch Utilities&Resources, a commercial cartel that the Reich family has possessed for generations. Monarch Utilities&Resources is in danger of bankruptcy because of its chief rival, the D'Courtney Cartel, headed by the older Craye D'Courtney. Reich suffers recurring nightmares in which a "Man with No Face" persecutes him.
Reich contacts D'Courtney and proposes a merger of their concerns but Reich's damaged psychological state causes him to misread D'Courtney's positive response as a refusal. Frustrated and desperate, Reich determines to kill Craye D'Courtney. The presence of peepers has prevented the commission of murder for more than 70 years so Reich devises an elaborate plan to ensure his freedom. If caught Reich will certainly face "Demolition", a terrible punishment described only at the end of the story.
Reich hires an Esper to "run interference" for him—hiding his murderous thoughts from any peepers present at the scene of the planned crime. Reich has many Class 2 and Class 3 Espers working for him but for this task he must hire a top Class 1 Esper. Reich bribes Dr. Augustus ("Gus") Tate, a prominent peeper psychiatrist, to be his mental bodyguard during the murder. Tate is a member of the "League of Esper Patriots" who believe in the innate superiority of Espers, and who advocate for a society where Espers are in charge. Reich is covertly funding the League. Tate helps Reich, stealing information about D'Courtney's whereabouts by peepingD'Courtney's personal physician, the Class 1 Esper Dr. Sam Atkins (@kins in the text). D'Courtney lives on Mars but occasionally visits Earth, always staying at the home of socialite Maria Beaumont. Tate learns that he will be there for one night, coinciding with one of Maria's notorious parties.
To further conceal his intentions from telepaths, Reich visits a songwriter, Duffy Wygand (spelled "Wyg&" in the text) who teaches him a deceptively simple jingle --
Eight, sir; seven, sir; Six, sir; five, sir; Four, sir; three, sir; Two, sir; one! Tenser, said the Tensor. Tenser, said the Tensor. Tension, apprehension,
And dissension have begun.
—that proves to be an earworm, so persistent and involving that it blocks most Espers from properly peeping into Reich's mind.
From Monarch's R&D facility, Reich secures a small flash grenade which can disrupt a victim's perception of time by destroying the eyes' rhodopsin. He also visits Jerry Church, an Esper who is shunned by his kind as punishment for helping Reich break the law. Jerry runs a pawn shop, in which Reich found an antique (20th-century) handgun, a rare object in a largely non-violent society. The gun is described as combining a stiletto knife, a knuckle-duster and a revolver in a folding package, an Apache revolver. To deflect suspicion, Reich has Jerry remove the bullets from the cartridges in the gun before he accepts it. He knows how to replace the bullet in the handgun's ammunition with a gelatin capsule filled with water in order to eliminate ballistics evidence.
To cover his movements at the party, Reich makes sure Maria organizes a game of Sardines to be played in total darkness. Tate having peeped the location of D'Courtney's room, Reich executes his plan during the game. However, there is an unforeseen hitch: the moment he shoots D'Courtney, D'Courtney's daughter Barbara, witnesses the murder, struggles with Reich, grabs the gun and runs away. She is later found suffering severe psychological shock that renders her catatonic and mute. Nobody but Maria knew she was with her father. Reich recovers his composure, returns to the party and pretends to be lost. Just as he is about to leave, completing his getaway, a drop of blood from D'Courtney's body in the room above lands on him, and the party ends in chaos as the police are called.
Police Prefect Lincoln Powell is a Class 1 Esper, a highly talented man expected to become the next president of the Esper Guild. He arrives as his partner, Jackson Beck (Esper 2) has set up a variation of "good cop - bad cop" with Powell as the "good" cop, to get past the suspicion of the louche crowd at the party. Powell meets Reich and immediately hits it off with him, partly due to Reich's charm but also because Powell senses a kindred spirit. However, Reich's Esper attorney is present, ostensibly to guard Reich's business secrets from unwanted peeping. Telepathically-gathered evidence is legally inadmissible in court, but can be used to guide an investigation. This obliges Powell to assemble the murder case with traditional police procedures and to establish motive, opportunity and method.
Even without telepathy, Powell knows Reich is guilty when he interviews the guests at the party about D'Courtney and Barbara. He focuses on Reich, who tries to be casual, saying to Powell: "The whole thing was crazy. If the girl was lunatic enough to sneak out of the house without a word and go running naked through the streets, she may have had her father's scalp in her hand." Moments later, Powell says to Beck, "Didn't you hear the slip when he was busy stiffing me? Reich didn't know there was a daughter. Nobody did. He didn't see her. Nobody did. He could infer that the murder made her run out of the house. Anybody could. But how did he know she was naked?" To check, Powell engineers some impromptu theater to distract Reich's Esper attorney long enough to peep the truth from Reich himself. He pulls Reich aside after promising not to peep him, and reveals what he knows. Reich is not surprised, saying he would have done the same. Powell asks him to surrender, but Reich refuses, relishing the thrill of the hunt to come. They part "with the four-way handshake of final farewell" and the contest between them begins.
Both sides center on finding and questioning (or, in Reich's case, silencing) Barbara D'Courtney. Although Reich finds her first he is unable to kill her before Powell rescues her. Powell loses Reich for a while. The pursuit traverses the Solar System as Reich escapes the police and a series of mysterious assassination attempts. Others are attacked also: during Powell's attempt to interrogate the Esper pawnbroker from whom Reich bought the gun, an unknown person attacks the pawnshop with a "harmonic gun" which kills by resonant sonic vibration. Reich tries but fails to murder Hassop, his chief of communications (to try to prevent him from assisting the police with his knowledge of the corporate codes) and Powell succeeds in abducting Hassop.
Powell has already established opportunity and, eventually, method through discovery of a tiny fragment of gelatin in the body. Just as Powell believes that he has wrapped the case up entirely the interrogation of Hassop yields disturbing results: D'Courtney had accepted the merger proposal. That dashes Powell's case; as he remarks, no court in the Solar System would believe Reich murdered D'Courtney when D'Courtney was needed alive for the merger (which would save Reich and give him all the power and wealth he dreamed of) to succeed.
Reich's tortured mental state is unknown to Reich himself so Powell does not suspect that the motive for the murder was something other than financial. After more attempts on his life, and more dreams of the Man with No Face, Reich attempts to kill Powell. Powell easily disarms him and then reads his mind. Suddenly Powell recognizes that the forces behind Reich's crime are greater than anticipated. He asks the help of every Esper in attempting to arrest Reich, channeling their collective mental energy through Powell in the dangerous telepathic procedure called the "Mass Cathexis Measure". He justifies this by claiming that Reich is an embryonic megalomaniac who will remake society in his own twisted image if not stopped.
Powell uses the power to construct a solipsistic fantasy for Reich to experience. One by one he removes elements of reality, beginning with the stars in the sky, until Reich is left believing that he is the only real being in a world constructed around him, as a game. Finally Reich is left facing the Man with No Face, who is both himself and Craye D'Courtney.
Reich is revealed to be the natural son of Craye D'Courtney, from an affair with Reich's mother— Reich's hatred of him was probably due to a latent, telepathic knowledge of that fact. Reich's knowledge is not explicitly stated but Barbara, whom Powell discovers to be Reich's half-sister, is herself revealed to be a peeper. The assassination attempts on Reich were carried out by Reich himself as a result of his disturbed state. Once arrested and convicted, Reich is sentenced to the dreaded Demolition— the stripping away of his memories and the upper layers of his personality, emptying his mind for re-education. This 24th-century society uses psychological demolition because it recognizes the social value of strong personalities able to successfully defy the law, seeking the salvaging of positive traits while ridding the person of the evil consciousness of the criminal.