Background: When predictive survival models are built from high-dimensional data, there are often additional covariates, such as clinical scores, that by all means have to be included into the final model. While there are several techniques for the fitting of sparse high-dimensional survival models by penalized parameter estimation, none allows for explicit consideration of such mandatory covariates. Results: We introduce a new boosting algorithm for censored time-to-event data that shares the favorable properties of existing approaches, i.e., it results in sparse models with good prediction performance, but uses an offset-based update mechanism. The latter allows for tailored penalization of the covariates under consideration. Specifically, unpenalized mandatory covariates can be introduced. Microarray survival data from patients with diffuse large B-cell lymphoma, in combination with the recent, bootstrap-based prediction error curve technique, is used to illustrate the advantages o...