In this talk, I will present results that are widening the scope of extreme value analysis applied to discrete-valued data containing many tied observations. Ex- treme values of a random variable X are commonly modeled using the generalized Pareto distribution, a method that often gives good results in practice. When X is discrete, we propose two other methods using a discrete generalized Pareto and a generalized Zipf distribution respectively. We will see that both are theoreti- cally motivated and that they perform well in estimating rare events in several simulated and real data cases such as word frequency, tornado outbreaks and multiple births.