We discuss a Fleming-Viot model whose mutation process is a birth- and death process on the non-negative integers. In this model, new deleterious mutations accumulate at a constant rate per generation, and each mutation decreases the individual fitness by a constant amount. Other than in the classical case of Muller's ratchet, each of the present mutations has a small probablity per generation to disappear. In the infinite population limit we obtain the solution in a closed form by analyzing a probabilistic particle system that represents this solution. We will also discuss recent ideas to approach (yet unsolved) questions on the rate of Muller's ratchet. The talk is based on joint work with Peter Pfaffelhuber and Paul Staab.