Summary. We propose ‘Dunnett-type’ test procedures to test for simple tree order restrictions on the means of p independent normal populations. The new tests are based on the estimation procedures that were introduced by Hwang and Peddada and later by Dunbar, Conaway and Peddada. The procedures proposed are also extended to test for ‘two-sided’ simple tree order restrictions. For non-normal data, nonparametric versions based on ranked data are also suggested. Using computer simulations, we compare the proposed test procedures with some existing test procedures in terms of size and power. Our simulation study suggests that the procedures compete well with the existing procedures for both one-sided and two-sided simple tree alternatives. In some instances, especially in the case of two-sided alternatives or for non-normally distributed data, the gains in power due to the procedures proposed can be substantial.