At the 1994 Winter Paralympics in Lillehammer, Norway, Stockford again competed in downhill, giant slalom, super-G and slalom events in a classification now renamed as LWX. He failed to finish in the downhill slalom or giant slalom but picked up his fourth Paralympic bronze medal in the super-G. Since this bronze, and the four others won by British athletes in Lillehammer, Britain has failed to win any Paralympic alpine skiing medals.