A top fashion model is found at a construction site, apparently shot to death. When it is discovered that she was drowned before she was shot, Burke tracks the case back to her ditzy landlady, and then to the heads of the ad agency she was modeling for and the artist who was painting her likeness for a giant ad campaign. Getting involved with another model, Burke soon discovers a plush hideaway owned by three Texas millionaires who ""entertain"" gorgeous young women poolside (where the murder may have taken place). Even though he uncovers a blackmailing butler and information that an older admirer had paid for cosmetic surgery for the model, Burke is suddenly stumped when it is revealed that the water in the dead girl's lungs had orange blossom bath salts in it and not chlorine from the pool.

The Grand Duke, Maximilian Karol Alexandrei Kadarian, collapses at a banquet. The Grand Duke was famous locally as phony royalty, who owned a fabulous emerald necklace, now missing. The suspects include his former wife, his secretary, the owners of the banquet hall (two former vaudevillians), the ghostwriter of his autobiography, a ""reformed"" safecracker, another Russian noble now working as a director, and the mysterious and elusive ""Charlie Prince"".

Promoter Harris Crown is killed when the car he is driving goes off a cliff. Burke soon discovers that all the brake fluid had been drained and that the car belonged to Crown's wife (a race car enthusiast) who is involved in a charity benefit and ""involved"" with the benefit's choreographer, who in turn is being kept by a wealthy (and jealous) society matron. Other suspects include Crown's strapped-for-cash brother and his greedy wife, and Crown's current mistress. Burke is assisted in his search for the killer by a gossip columnist and a shop owner (who takes a sudden shine to Burke, until she finds that he's a ""poor"" cop).

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When a body is discovered dumped alongside the merry-go-round at an amusement park, clues (including a phone number on an old matchbook cover) lead back to the elusive millionaire Emory Flood. Burke is thwarted in his attempts to speak to Flood by the top three men in the Flood empire. Meanwhile, Burke and Tim come to the aid of an elderly woman who is also trying to see Flood, and interview three lovely starlets who are being ""supported"" by Flood (two of whom hate the man, while the third definitely strikes romantic sparks with Burke). Until Burke can identify the dead man, discover the true scene of the crime and locate Flood, he can't find the killer. A photo of Robert Mitchum reveals the clue which proves that the crime was based on a case of mistaken identity.

Betsy Richards drinks a lethal martini and Burke investigates the Richards mansion, Betsy's three identical sisters (who may look alike, but who have decidedly different personalities), her wheelchair-bound (and possibly psychotic) aunt, her current beach bum lover (who might have been about to leave Betsy for another sister), her alcoholic brother-in-law, and a slightly demented professor of psychiatry. An attempt is made on the life of another sister and, after a second death, the dark secret of the Richards family is finally revealed.

A self-proclaimed witch sends Burke a record predicting her murder, along with a list of suspects. When her body is discovered after a fire, she has been disfigured by acid, leaving only a clue of a tattoo. The design of the tattoo matches that of an amulet carried by her pet raven. For likely suspects, Burke has to choose between a less-than-imposing ""vampire"", the head of a nudist colony, the ""reincarnation"" of the Goddess of Love, a wealthy man obsessed with spiritualism and his compliant companion, and a con artist/fakir. Before the case is solved, Tim saves Burke from a ""brush"" with death!

When an unidentified brunette is discovered in a fake electric chair at a run-down amusement park/sideshow run by ""Professor"" Kingston, Burke has to track several elusive clues back to a modeling agency and the three somewhat odd people who run it, a blackmail scheme, eloping tennis players, and a feisty old Irish landlady. With the help of a vital piece of information gathered by Burke's girlfriend Juliet and the assistance of three young boys, the case is solved.

During Chinese New Year celebrations, a car crashes into a street full of revelers. After the Chinese woman behind the wheel flees the scene with a little girl, leaving behind her shoe, a tourist discovers a dead body in the trunk. Tracking the case to the nearby nightclub The Paper Dragon, run by Burke's old friend (of ""very mixed"" Chinese and Irish extraction), Burke tries to discover if the club's dancer is the killer or the next victim. A local drunk ventriloquist, the dead man's wife, and a shifty promoter round out the suspects.

A rose-covered cottage is the scene for the death of a seemingly ordinary housewife. Burke and Tim (who is contemplating settling down with his current girlfriend) soon discover that all is not what it seems in suburbia. The dead woman's husband, her totally gaga neighbor, a stripper with a boa constrictor, a flustered physician, several predatory landladies, a tennis bum, a couple of wigs, and the surly head of the Burglary Division all help to turn what at first seemed like just a slip in the bathtub into one of Burke's more complicated cases.

When an old flame of Burke's is gunned down, he uncovers the darker side of her relationship with several men. The former chauffeur for the victim's father, an old friend of the family, an philandering astronomer and his embittered wife, a free-wheeling B-girl, a vulgar jazz trumpeter - any one could have killed ""my girl"". The truth may lie in Diana's little black book. Les and Tim are worried that Burke is too close to the case to handle it rationally. Burke refuses their help. Only after he is attacked in his own home and, later, is forced to hear the truth about Diana's past, does Burke realize who the killer is, with the help of Les's wristwatch.

A notorious homewrecker is discovered dead in a mud bath at a fashionable spa. Burke soon learns that every other guest at the spa, including the owner, had a strong motive for murder. The strongest case is against the woman whose husband might have been planning on divorcing her to marry the victim. A movie starlet, the best dressed woman in the U.S., a millionairess and her aunt/companion, and the spa's owner also need to be carefully watched. Even after Burke is viciously attacked, he puts himself in danger again in order to smoke out the real killer.

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When big-game hunter Cable Roberts is found shot by one of his own rifles and ""mounted"" in his trophy room, the suspects include both Roberts' current wife (a predatory animal herself), his ex, an angry taxidermist, another hunter, Roberts' secretary, and his extremely sexy maid. Tim notices an interesting point - that Roberts was killed in the same way in which he killed his big game. After two false confessions, Burke discovers that one of the suspects has a more complex relationship to Roberts than first appeared.

When millionaire Wade Walker's plane explodes mid-air, Burke confronts Walker's business partner, secretary (whom Tim has an eye for), and the four women in his life (a model and beauty pageant queen, a society horse breeder, a starchy, sex-obsessed nurse, and a nightclub singer), one of whom Walker may have proposed to just before he died. All of Burke's theories go up in smoke when it is discovered that Walker died of an overdose of morphine before the plane blew up.

Tim's mother is in town for a visit and provides several vital clues that solve the murder of April Adams. Tracking the victim to a carhop-style restaurant, Burke narrows the suspects to April's erratic brother, her cousin, her psychiatrist, the drive-in restaurant's manager, and a hockey star and his wife. Empty sugar packets from the drive-in and several bankbooks provide Burke with the link to a drug deal.

After a party celebrating his marriage to an Italian movie starlet, producer Marty Kelso falls down a flight of stairs and gets a letter opener stuck in his neck. His bodyguard/manservant calls the police and informs Burke that Kelso's three ex-wives (a former Olympic star, a screenwriter and a failed actress) were at the party, along with the Olympic star's surly husband and a film director. Clues pop up at the oddest times and in the most curious places. Les and George each claim the other overlooked vital information. Several people had good motives to murder Kelso, but Burke knows that just because a suspect seems obvious doesn't mean there might not be a set-up in the works.

Hemingwayesque novelist Julian Buck is found dead and Burke checks out the guests at his funeral: his publisher, a former boxer, an ex-lover (who he ""traded"" for a plot), a bartender, a crippled university professor, and a glamorous blonde, all of whom have been used in the past by Buck as fodder for his plots. The manuscript of his latest novel (also based on facts from Buck's life) probably will contain the vital clue that will lead to the murderer.

At the opening of The Debonair Key Club, a Playboy-like nightclub/restaurant, Debonair Magazine founder Alex Debbs is found stabbed. The suspects are all connected in some way with the Debonair empire, both the club and the magazine: Debbs' main business partner, an embittered cartoonist, a swinging joke writer, a blackmailed princess, a folk guitarist, one of the Key Club girls, and a reclusive heiress. After an attack on Tim, another murder and the breaking of ""unbreakable"" alibis, Burke solves the case.

A missing Siamese cat named Deborah is Burke's prime clue to the killing of Cynthia Royal. The murder victim had just arrived in town from Chicago trying to reunite with her estranged husband. The husband had been wooing a nightclub singer, which leads Burke also to suspect the nightclub's owner/comic and his attorney. When Burke and an elderly acquaintance stumble across another body, the trail eventually leads to two beatniks, the return of Deborah and the solution of the case.

Burke is attending a pool party at tycoon Victor Haggerty's mansion when dashing Beau Sparrow is thrown into the pool by a faulty diving apparatus and dies. The apparatus doesn't seem to have been tampered with and George McLeod can't determine the cause of death. Was it murder? If so, who's the killer: the tycoon, his spoiled pampered wife, her paid companion, the countess who was Beau's current flame, the tough-as-nails secretary, or the blowhard businessman? As soon as Burke figures out who the culprit is, he has to rush to prevent another death.

When the president of a bank is shot during a robbery, the only description Burke can get of the killer is that he was ""just ordinary"". Burke interviews a man who passed out during the robbery, and hunts for clues with a local bookie. After the two other bank robbers are slain, Burke investigates the bank president's wife and son, his very flirtatious secretary, his business partner and his accountant, and a beautiful B-movie star. Just as Burke is about to arrest the man who shot the bank president, the killer is himself slain - but by whom? And why?

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Psychiatrist Eric Techman calls Burke to report that he fears one of his patients is a homicidal maniac who plans to kill him. Before he can identify the person in question, he is shot in the back. Burke convinces both Techman's secretary and his wife to not reveal the fact of the kind doctor's murder until Burke can question the five most likely patients: a stripper, a movie starlet, a Texas oil millionairess and her wild son, and a ski instructor (and sometime kleptomaniac).