Let κ \kappa , λ \lambda be cardinals, κ ≥ ℵ 1 \kappa \geq {\aleph _1} and regular, and 2 ≤ λ ≤ κ 2 \leq \lambda \leq \kappa . If κ > ℵ 1 \kappa > {\aleph _1} and λ > κ \lambda > \kappa , and if there is a κ \kappa -Suslin ( κ \kappa -Aronszajn, κ \kappa -Kurepa) tree, then there are 2 κ {2^\kappa } normal λ \lambda -ary rigid nonisomorphic κ \kappa -Suslin ( κ \kappa -Aronszajn, κ \kappa -Kurepa) trees. If there is a Suslin (Aronszajn, Kurepa) tree, then there is a normal rigid Suslin (Aronszajn, Kurepa) tree. If there is a κ \kappa -Canadian tree, then there are 2 κ {2^\kappa } normal λ \lambda -ary rigid nonisomorphic κ \kappa -Canadian trees.