Souray's offence began to improve following his trade to the Canadiens. At the time of his trade from the Devils, he had just eight points, all assists. He finished with three goals in 19 games as a Canadien to tie his career best for goals in a season, and establish a new career best for points (11) in 71 combined games. More importantly, he began using his dangerous shot more often once he arrived in Montreal. In 2000–01, injuries limited him to just 52 games, 19 less than the previous year, but Souray still managed to match his previous season's career bests in goals (3), assists (8) and points. He got off to a good start in 2001–02, threatening to surpass his previous offensive highs, as he tallied three goals and five assists in just 34 games while fighting through an injury-plagued campaign. 2001–02 also saw him record his first career power play goal, as the Canadiens began to realize the value of having a player on the point who could consistently shoot the puck as hard as Souray. However, he suffered a wrist injury that plagued him throughout the year, and though he would play through it much of the season, Souray would eventually shut it down at the end of the season.