Many studies involve comparisons of multiple treatments with a control, in terms of certain response variables. In such cases, the Dunnett test is often used for strong familywise error rate (FWER) control, where the critical values are determined based on the multivariate T distribution with correlation structure specified according to the study design. When the response variables are discrete, the Dunnett test can be very conservative. In this study, we consider alternative, single-step and stepwise, multiple testing procedures for discrete response variables that are based on the exact joint distribution of the discrete test statistics. The proposed procedures incorporate both dependency and discreteness of the test statistics and therefore improve the Dunnett test. The results under both the balanced and the unbalanced study designs are explored. Performances of the proposed procedures are investigated through simulation studies and a real data application.