Back in 2012, a team of archaeologists discovered the extremely old bones of a man with a twisted spine buried in an unassuming parking lot in Leicester, 100 miles northwest of London. After DNA analysis subsequently identified the remains as those of King Richard III, killed in battle in 1485, they were laid to rest amid much ceremony in a new tomb at Leicester Cathedral in March 2015. This week, archaeologists began searching underneath yet another parking lot–this one in Reading, England–for the long-lost remains of another British monarch, King Henry I.

The youngest of four sons born to King William I (better known as William the Conqueror), King Henry I ascended to the throne in 1100, after the death of his older brother, William II, in a hunting accident. He acted quickly to seize power, taking advantage of the fact that another older brother, Duke Robert Curthose, had left England on the First Crusade.

Henry proved to be an effective, if repressive, ruler, strengthening the monarchy and establishing a rigid administrative system that kept the realm functioning efficiently. He also stood out for his rampant womanizing; he fathered some two dozen illegitimate children, more than any other British monarch in history. In one gruesome incident, Henry is said to have let two of his own granddaughters be mutilated (their eyes poked out and the tips of their noses cut off) as part of a political quarrel.

In 1135, King Henry died of food poisoning after gorging himself on lampreys, an eel-like, jawless fish that was one of his favorite delicacies. His body, stitched inside a bull’s hide, was transported to Reading Abbey, 40 miles west of London. At the time, Reading was a religious center and one of England’s most important medieval towns. Henry himself had founded the abbey there, and it was among the grandest in medieval England. According to burial records, the king was laid to rest beneath the high altar.

Some four centuries later, Reading Abbey would be destroyed almost completely–and the location of Henry I’s tomb lost to history–after King Henry VIII ordered the dissolution of all England’s monasteries in the 1530s. Most of the old abbey’s remains are known to lie underneath the grounds of Reading Prison, a penitentiary immortalized by its onetime inmate Oscar Wilde in his famous poem “The Ballad of Reading Gaol.”

Now, a team of historians and archaeologists are using ground-penetrating radar to search underneath the prison’s parking lot, as well as the area around a nearby nursery school. Based on calculations about the size of the old Reading Abbey and its footprint, they believe these areas to be closest to where the old abbey’s high altar would have been located. John Mullaney, one of the historians conducting the search, told the New York Times that archaeologists know Henry’s probable burial place “within a few yards.”

Also spearheading the Reading project is Phillippa Langley, who led the search four years ago for the remains of King Richard III, discovered under the parking lot in Leicester. The controversial last king of the Plantagenets was killed at the Battle of Bosworth in 1485 and buried by his enemies; his grave had remained unmarked and unknown for more than 500 years. Since Richard’s remains were reburied in a ceremony at Leicester Cathedral in March 2015, his tomb has become a popular tourist attraction, and supporters of the new search project hope that finding the remains of another king may bring the same kind of attention to Reading.

If they do succeed in locating the remains of King Henry I, the researchers will face another difficult hurdle when it comes to verifying them through DNA testing. It was easier in the case of Richard III, as scientists managed to extract DNA exactly matching two descendants of his sister. But Henry I lived and died more than 350 years earlier, and any living descendants would have to be traced through one of his many illegitimate children, or his mother’s line.

“We were quite lucky with Richard because of the genealogical evidence, but the further back you go the less reliable it becomes,” Dr. Turi King, a lecturer in genetics and archaeology at the University of Leicester who carried out the DNA testing on Richard III, told the Guardian when the Reading search was announced last year.

Still, the team working on the current project hopes their search will bear fruit, if only for the sake of giving King Henry I, like Richard III, a burial more appropriate to an English monarch. “Henry was a reforming king and would have been fascinated by the idea of cars and transport, and may well have liked being buried under a car park,” Mullaney told the Times. On the other hand, he continued, “He was a religious man and so I think he would have preferred being buried in a church.”