Summary: This paper studies the special case of the triangular system of equations of E. Vytlacil and N. Yildiz [ibid. 75, No. 3, 757–779 (2007; Zbl 1130.62111)], where both dependent variables are binary but without imposing the restrictive support condition required by Vytlacil and Yildiz for identification of the average structural function (ASF) and the average treatment effect (ATE). Under weak regularity conditions, we derive upper and lower bounds on the ASF and the ATE. We show further that the bounds on the ASF and ATE are sharp under some further regularity conditions and an additional restriction on the support of the covariates and the instrument.