We present a general and path-consistent wrong-way risk (WWR) model, which does not require simulation of credit and market variables simultaneously. Although similar so-called copula models are well known, our approach is novel in several ways. First, our method can model a wide range of dependence structures while always guaranteeing path consistency of default probabilities (the possibility of path-inconsistencies in copula models was highlighted in a recent article). Second, we place special emphasis on the difficult task of calibrating the underlying dependence structure. In particular, we consider a default correction of the dependence structure. Third, our model serves as a bridge between structural model approaches, where dependence between exposure and equity price is modeled, and copula models, where exposure is directly correlated to default time. Finally, we apply our method in realistic situations and show that we can achieve a wide range of WWR impacts.