At a highway construction project, a giant earth mover is shifting landfill near some giant tires which are being lifted out of the way of the construction. Suddenly, one of the workers notices the nude body of a blonde inside one of the tires.
Burke is saying goodbye to the last guests at a party hosted at his mansion. His girlfriend Sophia and he get cozy, as she tries to pin him down to a time for their date the next day. A call from Lt. Joe Nolan calls him to the crime scene.
The unidentified victim had been shot around midnight with a .38. Special notice is made of her newly capped teeth. Tim Tilson, Les Hart's new partner, has anticipated Burke's every request and has even kept track of Burke's impending schedule for that day. When one of the construction workers wonders why someone riding in a Rolls would be a cop, Tim asks him why he's a construction worker. When the man replies that's what he does best, Tim says that's why Burke is a cop.
At the station, Burke banters with Bill, the desk sergeant. When Burke makes a crack about Bill's age, Bill says he can lick Burke any time. Burke replies:
NEVER BOX WITH A SENIOR CITIZEN - BURKE'S LAW.
Nolan reports a lucky find of the victim's dentist. She is Holly Howard. Her teeth were capped very recently and the bill was paid in full, in cash.
At the boarding house where Holly stayed, the elderly landlady Mrs. Bowie tells Burke Holly had moved away 2 months before. She was a "lovely" girl who liked "Mr. Demille", who turns out to be Mrs. Bowie's tomcat. Cecil B. DeMille discovered Mrs. Bowie in a pharmacy and gave her a screen test, then employed her in small roles over the years, so she named the cat after him. She gives Burke Holly's forwarding address, in a much fancier neighborhood.
At the new apartment, Holly's modeling portfolio is found, indicating the Planet Agency employed her. At the agency, the woman in charge mistakes Burke for the model in the beer commercial being shot with several bathing beauties, asks him to strip and then says he won't do. When he identifies himself, she tells him Holly had only been there a month and only had one job, with Nickerson and Greene ad agency. As Burke leaves, a model asks him for a lift to the agency.
The model, Bridget Jenksins, admires Burke's car and flirts. He gets her address and phone number; she tells him she knew Holly and used to go swimming with her up in Lido Hills at a home, where she didn't know the owner, who never seemed to be there. She says Holly was nice but odd; she gave people gifts all the time if she liked them. Burke gets word that Ed Nickerson, head of the agency, is at a sign studio firm, so he drops Bridget off (after making a dinner date) and goes on. Bridget is disturbed when Burke tells her Holly was shot.
At the painting workshop, Nickerson and his assistant, McNulty, are upset when they find out that Holly is dead, because the whole ad campaign (for "Cherchez La Femme" cosmetics) was based on her, with billboards and TV and personal appearances. Now they'll have to find another girl. Nickerson tells Burke he picked Holly personally. She was shy and prim. He saw her a week ago, when she gave him a lighter as a gift. At first he quibbles when Burke asks him for an alibi for the night before. Then he admits that he and his wife went to dinner with the "Cherchez" client, then his wife went home with a headache, and he went to the beach with the client (who is female). He says he could never have hurt Holly. The billboard painter, Fred Hopke, when told he will have to repaint everything because Holly was killed, says "good", because that will mean more overtime.
Tim gets the M.E. report which indicates Holly was dead when she was shot, and in fact had been drowned.
At Bridget's apartment, Burke finds out the address of the pool where the girls used to swim. He offers to give Nickerson a on Bridget's behalf, since the agency will need a new girl. Bridget offers to make Burke breakfast, but he has work to do.
NEVER EAT NICE LITTLE PANCAKES WHEN YOU'RE IN A HURRY - BURKE'S LAW.
At the pool address, Les is interviewing several bikini-clad girls. When they realize how many police are there, two girls discuss getting out of there. No one lives in the house. The only occupant is the butler, John Busch, who claims not to know who owns the house. The building is registered out of Houston to Tri-M Investments, whose treasurer is Harry Jo Murdock and whose two other officers are Vaughn Moore and Thomas Mathewson. When Burke asks about finances, Tim tells him Murdock is the poorest of the three, having "only" twelve million dollars. The three apparently use the place as a hotel when they're in town. Burke tells Tim to wire Houston and make sure all three come to L.A. He figures, with all the girls around, since all three men are married, they won't object.
Busch insists there are no guns on the premises. His room is covered with photos of birds and the bathroom is a darkroom. He says he photographs the birds from his window (which overlooks the pool) when they come to drink. When told of Holly's death, he says "God gave and God has taken away". Les wonders why the birds would drink water full of chlorine. When Busch says that one bird he has photographed is a Colima warbler, Tim tells Burke that the Colima warbler is only found in the mountains of Texas. Burke accuses Busch of taking other types of photos and has him taken to the station. When Busch tries to take his Bible, Burke confiscates it and tells Tim to gather up all the photos and negatives in the house.
Inside the bible are found other negatives, which turn out to be photos of two men poolside in compromising positions with two girls.
The three Texans arrive, in suits, string ties, ten-gallon hats and silver-toed cowboy boots. Tri-M is a holding company with interests in oil and real estate. They admire Burke's house and car and wonder how much L.A. cops get paid. Moore and Mathewson are the two men in the Busch photos. They finally agree to talk to Burke when he threatens to expose them to their wives. Moore and Mathewson insist they didn't know Holly, hadn't been to the house for two montht, and were at an oil association dinner together with their wives when she was killed. Murdock admits to knowing her "slightly", was at the house a month ago, but says he had flown down to Baja and was fishing when Holly was killed. Burke lets Moore and Mathewson know Busch was setting them up for blackmail and orders them all to stay in town.
Personally Burke can't figure out why there's no picture of Murdock, until Tim realizes he forgot to check the camera on the tripod in Busch's room. Burke tells him to go back with Les and check.
IN CASES OF HOMICIDE, CHECK OUT THE FACTS, ONE BY ONE, SLOW AND EASY - BURKE'S LAW.
Tim goes alone and surprises an intruder, who clubs him over the head with a flashlight. Tim chases him and catches him on the stairs. Burke arrives just in time to see that the intruder was indeed Murdock.
Busch was such a tightwad that he didn't want to waste film and was waiting to finish the last roll before blackmailing the three Texans. Busch insists there's no evidence of any blackmail, but Burke has him arrested as an accessory after the fact. Burke figures Busch found Holly's body in the pool, shot her to confuse the issue and moved her to the construction sight. He tells Busch that, at the least, he's guilty of being a litterbug.
Murdock admits he had been having an affair with Holly and had not been fishing in Mexico, but was indeed in his plane on the way back to Houston after seeing her. Burke finds this was true. Murdock also denies knowing anything about either Holly's capped teeth or the nose job she had recently had done. He insists Holly was a nice girl and had never threatened to expose him to his wife.
Back at the boarding house, Mrs. Bowie tells Burke she's having trouble renting Holly's room. She also points out that she has trouble with Hopke, who lives just down the hall from Holly's old room. When Burke greets "Mr. DeMille", Mrs. Bowie curtly informs him that this cat is "Tom Mix".
Hopke is a very skilled artist, in addition to his job, and has dozens of canvases in his room. Hopke tells Burke Holly was ugly until she had her teeth capped and nose fixed. She moved out of the boarding house as soon as the bandages came off. He doesn't know who paid for the plastic surgery. When they admire his artwork, Hopke scoffs and says how could he possibly get a one-man show in this town with its philistine atmosphere. He insists art is not a business and asks them to leave him alone.
Tim has a theory; he thinks Hopke is the killer, because he was in love with Holly and paid for the surgery, then was dumped by her. Tim gets angry when Burke doesn't back him up.
MY THEORY ABOUT THEORIES IS THAT YOU START OVER IN THE MORNING.
Tim asks Burke if that means he shouldn't think.
YOU CAN THINK, BUT NOT IN MY EAR.
Tim asks if this is another BURKE'S LAW and threatens to turn in his request for a transfer. Burke, equally peeved, says fine. Les interrupts them to reveal a new report from the M.E. that shows Holly wasn't drowned in any pool - no chlorine in the water. Probably was drowned in her bath and the water that killed her had orange blossoms in it.
Tim goes to a nightclub, the Glass Hat, to see McNulty. When he tells McNulty that his wife told Tim where he was, the girl McNulty is with at the bar stalks off. McNulty says Hopke was their only painter and usually worked way into the night alone, since they were behind schedule on the ad campaign. Hopke has his own key and could have come and gone at any time. Hopke had gotten a large advance before starting the job, McNulty says, because a friend needed surgery. Tim leaves a message with Bridget to tell Burke he has solved the case and is going to pick up the killer.
Bridget greets Burke in her bubble bath. He's right on time for their date.
ALWAYS PUNCTUAL WHERE BEAUTIFUL GIRLS ARE CONCERNED - BURKE'S LAW.
Bridget thanks Burke for getting her the agency job. Burke says Nickerson told him she already had it when he called. Burke smells orange blossoms. Bridget shows him the sample Nickerson had given her as part of the ad campaign.
Burke rushes to Holly's house and finds the exact same bottle of bath salts. He also sees a painting of her done by Hopke on the wall and suddenly knows who the killer is.
Tim finds Hopke painting the new giant billboard of Bridget's face. He accuses Hopke of killing Holly. They fight, Hopke knocks out Tim and is about to club him to death when Burke arrives. Hopke runs up on the catwalk to escape. He says he paid for Holly's surgery and teeth because he loved her and thought she was beautiful underneath, but she left him for that Texas millionaire. Hopke says he was the only one who cared about her, but she was ugly clean through. He loses his balance and falls; the giant billboard he had painted of Holly topples, crushing him to death. Burke realizes Bridget is in the shadows and turns a floodlight on her. He accuses her of the murder. She knew the modeling job was available even before Holly's death was announced (Burke had given her the ride to the agency). Holly was modest and would only have allowed a woman into her bathroom. Bridget drowned her and then let Hopke in so he could move the body to the swimming pool (she knew he wanted revenge). Burke says she was coming then to warn him. Briget says he has no proof, especially now that Hopke is dead. She kisses him passionately and tells him how they were meant for each other and could have a wonderful time together. Les and Joe arrive. Les asks if they're interrupting anything. Burke says he was just saying goodbye and tells Les to book Bridget for murder.
She asks "another BURKE'S LAW"? Burke says yes, BURKE'S LAW. As she is led away, Bridget takes one last look at the the giant billboard of her image.
Back at the station, the report of another murder, aboard a Swedish freighter, comes in. Tim says the freighter is Norwegian. Turns out he is the only one who speaks a Scandinavian language (Danish) but he wants his transfer processed. Burke refuses and is about to send him off. Just then, Sophia arrives and says she speaks Norwegian. When she speaks, Burke asks her what she said - "I'm with you". Tim insists that what she was speaking was Danish. Burke says "close enough" and goes off with her to solve another crime.