In this paper we develop procedures for obtaining confidence intervals for the parameters of a Laplace distribution as well as upper and lower γ probability tolerance intervals for a proportion β, given a Type-II right censored sample from the Laplace distribution. The intervals are obtained by conditioning on the observed values of the ancillary statistics. The intervals are exact, and will generalize the work of Kappenman (1975, 1977) who considered the full sample case.