Relative survival methods used to estimate the excess mortality of cancer patients rely on the background (or expected) mortality derived from general population life tables. These methods are based on splitting the observed mortality into the excess mortality and the background mortality. By assuming a regression model for the excess mortality, usually a Cox-type model, one may investigate the effects of certain covariates on the excess mortality. Some covariates are cancer-specific whereas others are variables that may influence the background mortality as well. The latter should be taken into account in the background mortality to avoid biases in estimating their effects on the excess mortality. Unfortunately, the available life table might not include such variables and, consequently, might provide inaccurate values of the background mortality. We propose a model that uses multiplicative parameters to correct potentially inaccurate background mortality. The model can be seen as an extension of the frequently used Estève model because we assume a Cox-type model for the excess mortality with a piecewise constant baseline function and introduce additional parameters that multiply the background mortality. The original and the extended model are compared, first in a simulation study, then in an application to colon cancer registry data.