[4] He also served Rufus as a judge, and the historian Norman Cantor calls him a justiciar for Rufus,[5] but the historian Francis West, who studied the justiciar's office, notes that his one of appearance as a royal judge concerns his diocese, and that Luffa probably was mentioned only because he was expected to enforce the decision.[3][7] Under King Henry I, William's younger brother and successor, Luffa took little part in the Investiture Crisis in England.In 1106, Luffa did sign a letter to Anselm written by William Giffard Bishop of Winchester-elect that begged the archbishop to return to England from his exile.[14] However, this view has been challenged by the art historian R. D. H. Gem, who argues that because of the conservative nature of the architecture it was more probably begun under Luffa's predecessor, Stigand, who was bishop from 1070 to 1087, and who oversaw the transfer of the seat of the bishopric from Selsey to Chichester.[16] The art historian George Zarnecki has argued that the rood screen in the cathedral also dates from Luffa's episcopate.