A few months later, two more surfer girls, just 15, disappeared after catching a ride in Galveston near Stewart Beach.
All four were killed, their bones and remains later found in marshy bayous.
"There were just so many girls missing," said former Brazoria County Sheriff's Lt. Matt Wingo, who in 1981 counted a string of at least 21 girls who had ended up dead since 1971. Many had been shot and their badly decomposed or skeletal remains later found, mostly in remote marshes and fields.
For a while, Wingo recalled, the area "was a dumping ground."
One man was sent to prison for the murders of Johnson and Shaw.
But 40 years later, investigators speculate that not only is it possible that the wrong person was convicted, but the killer or killers responsible for a series of unsolved slayings in Galveston, Harris and Brazoria counties never paid for the crimes.
Johnson's skull was found in Clear Lake in early 1972, not far from where Shaw's remains were recovered with bits of cloth and a surfer's cross.
But Johnson's body never was found -- or so it seemed.
Today, forensic investigators are trying to determine whether the headless corpse of a 13- to- 15-year-old recovered 40 years ago a half-mile from Johnson's skull in the same bayou might be hers. Working on a theory by Galveston police officer Alfred Paige, investigators suspect the body may have been mislabeled, as a male, and subsequently remained unidentified.
DNA samples from Johnson's younger brother and the eventual exhumation of the unidentified body could resolve part of the mystery.
But linking the old cases to the nameless corpse also could breathe new life into police theories about whether their deaths were related to the other unsolved cases.
Wingo told the Chronicle he never was sure whether one or several killers were responsible for the all the murders.
Now retired, he's frustrated that he didn't assemble enough evidence for an arrest, though there were promising suspects, including a sheriff's son from Hondo, a Florida drifter and a murderer jailed for a different crime.
Little remains of the groovy surf-and-ski enclave just north of the 61st Street bridge in Galveston from which Johnson and Shaw disappeared. The girls lived in Webster, then a sleepy bay town of 1,500, and were among the first to disappear.
Glenda Willis, now 56, was friends with the 14-year-olds and says they went to Wix water ski school on Aug. 4, 1971, but the wind had made the bayou too rough for skiing. She later saw the girls at the beach, but told the Chronicle they weren't ready to go home when Willis packed up the orange Cougar XR7 she was known for back in the day.
"I was the one with the credit card and the hot rod car that hauled everybody around," she remembers.
Instead, her friends headed back to Wix and the island party scene on the shores of Offatts Bayou. That was the last she saw of them.
The surf-and-ski area where the girls were headed has since been wiped out by waves of redevelopment and hurricanes. Gone are Jericho Surf Shop, Wix water ski school and cheap weather-beaten rentals that attracted perpetually partying crowds of surf dudes, beach bunnies and trick skiers.
But in 1971, the pair hung out there, often hitchhiking home on the two-lane coastal highway that then linked the beach to Webster and other towns around Clear Lake.
When Shaw and Johnson disappeared, their parents reported them missing. Willis and other friends assumed they'd run away to California.
"They were tomboys and totally fearless," Willis said.
Two tropical storms hit the coast that fall, battering the marshes and sending silt and floodwaters spiraling through the bayous around Clear Lake.
In September 1971, only a month after the girls disappeared, the first teen's corpse was found floating in Taylor Bayou headless and clad in a Jericho Surf Shop T-shirt. Investigators for nearly a year believed the body was that of a missing Pasadena boy, until he unexpectedly came home. He'd run off and enlisted in the military under a false name.
The so-called John Doe's estimated date of death was early August: the same month Shaw and Johnson vanished.
Willis and Johnson's family members told the Chronicle they didn't know about the body, nor did they ever view it. Willis said she would have recognized the faded purple T-shirt as one of Johnson's.
A review of autopsies and forensic reports from 1971 and 1972 show that an assistant Harris County medical examiner apparently never considered that the first corpse might be Johnson's. In a sworn statement later, though, he conceded that decomposition was so advanced he could not rule out the possibility that the surfer might be a girl.
In November 1971, Maria Johnson and Debbie Ackerman, Galveston Islanders and regulars at Wix ski school, disappeared. Their bodies turned up in a bayou in Texas City. They had been raped and shot to death.
Wingo and other investigators wondered if the killer they sought had deliberately targeted girls in pairs.
In January of 1972, youths trolling the shallow waters of a coastal bayou north of Taylor Lake in boats spotted what looked like a volleyball. One waded over and found a skull.
About a month later, a passer-by found more bones in the same marshy area. By late February, dentists and forensic experts had identified Shaw's remains and Johnson's skull using dental X-rays.
Johnson, who preferred "Renee," was well-known in Webster at the time she vanished. Her grandfather was a city councilman who later became mayor. In June 1972, Webster police announced they had solved the case, blaming her death and Shaw's on Michael Lloyd Self, a brain-damaged mechanic who lived in Clear Lake.
But from the start, the murder investigation was tainted. Two Webster officers who arrested Self were later convicted of bank robbery. One obtained Self's two conflicting confessions through Russian roulette and threats, court records and testimony from other officers shows.
Several of Johnson's family members are convinced of Self's guilt.
Others are not.
"There was a great concern the system had blamed the wrong person," said Clinard J. Hanby, a defense lawyer who worked on Self's federal appeals and at one point persuaded a federal judge to set Self free. His release was later overturned by the Fifth Circuit Court of Appeals, and Self died in prison in 2000.
Even former Harris County prosecutor Douglas O'Brien, who worked the case, became convinced the wrong man went to prison and the true killer remained unpunished.
It was after Self's death that Galveston police officer Paige began re-investigating the 1971 disappearances. Paige believes a serial killer committed the murders of the four girls abducted from Galveston in 1971, and likely others.
Willis, their friend, just wishes they'd gotten in her Cougar that day: "There's never been closure for me."