Data-driven models are now deployed in a plethora of real-world applications — including automated diagnosis — but models learned from data risk learning biases from that same data. When models learn spurious correlations not found in real-world situations, their deployment for critical tasks, such as medical decisions, can be catastrophic. In this work we address this issue for skin-lesion classification models, with two objectives: finding out what are the spurious correlations exploited by biased networks, and debiasing the models by removing such spurious correlations from them. We perform a systematic integrated analysis of 7 visual artifacts (which are possible sources of biases exploitable by networks), employ a state-of-the-art technique to prevent the models from learning spurious correlations, and propose datasets to test models for the presence of bias. We find out that, despite interesting results that point to promising future research, current debiasing methods are not ready to solve the bias issue for skin-lesion models.