[en] We report on a Monte Carlo study of the three-dimensional bond-diluted 4-state Potts model which, in the pure case, undergoes a strong first-order phase transition. Subject to quenched, random disorder one expects a softening to a continuous transition from a certain disorder strength on. Employing a combination of cluster algorithms, multicanonical methods and reweighting techniques, we obtain strong numerical evidence for the existence of a tricritical point separating the first- and second-order regimes and give an estimate of its location