 In 1982–83, he set career highs of 13 goals and 24 assists for 37 points, while establishing himself as a top-notch penalty killer and face-off specialist.After four years with the Sabres, Peterson was claimed by the Vancouver Canucks in the 1985 NHL Waiver Draft.In 1985–86, he registered 9 goals and 22 assists for 31 points with the Canucks, including a career-high 3 shorthanded goals.