We provide an efficient and unbiased Monte-Carlo simulation for the com- putation of bond prices in a structural default model with jumps. The algorithm requires the evaluation of integrals with the density of the first- passage time of a Brownian bridge as the integrand. Metwally and Atiya (2002) suggest an approximation of these integrals. We improve this approx- imation in terms of precision. From a modeler’s point of view, we show that a structural model with jumps is able to endogenously generate stochastic recovery rates. It is well known that allowing a sudden default by a jump results in a positive limit of credit spreads at the short end of the term struc- ture. We provide an explicit formula for this limit, depending only on the L ́evy measure of the logarithm of the firm-value process, the recovery rate, and the distance to default.