The mesh adaptive direct search (MADS) algorithm is designed for blackbox optimization problems for which the functions defining the objective and the constraints are typically the outputs of a simulation seen as a blackbox. It is a derivative-free optimization method designed for continuous variables and is supported by a convergence analysis based on the Clarke calculus. This work introduces a modification to the MADS algorithm so that it handles granular variables, i.e. variables with a controlled number of decimals. This modification involves a new way of updating the underlying mesh so that the precision is progressively increased. A corollary of this new approach is the ability to treat discrete variables. Computational results are presented using the NOMAD software, the free C++ distribution of the MADS algorithm.