Kammala jumla mai zuwa: St. Louis Blues ne suka zaɓa Dwyer a zagaye na 3, na 67 gaba ɗaya, na NHL Entry Draft na 1996. Ba za a iya cimma yarjejeniyar kwangila tare da St. Louis ba, Dwyer ya sake shiga aikin a
1998 kuma Montreal Canadiens ne suka zaba shi a zagaye na shida, na 152.