A growing number of weak- and unsupervised machine learning approaches to anomaly detection are being proposed to significantly extend the search program at the Large Hadron Collider and elsewhere. One of the prototypical examples for these methods is the search for resonant new physics, where a bump hunt can be performed in an invariant mass spectrum. A significant challenge to methods that rely entirely on data is that they are susceptible to sculpting artificial bumps from the dependence of the machine learning classifier on the invariant mass. We explore two solutions to this challenge by minimally incorporating simulation into the learning. In particular, we study the robustness of Simulation Assisted Likelihood-free Anomaly Detection (SALAD) to correlations between the classifier and the invariant mass. Next, we propose a new approach that only uses the simulation for decorrelation but the Classification without Labels (CWoLa) approach for achieving signal sensitivity. Both methods are compared using a full background fit analysis on simulated data from the LHC Olympics and are robust to correlations in the data.