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Cost-sensitive feature selection describes a feature selection problem, where features raise individual costs for inclusion in a model. These costs allow to incorporate disfavored aspects of features, e.g. failure rates of as measuring device, or patient harm, in the model selection process. Random Forests define a particularly challenging problem for feature selection, as features are generally entangled in an ensemble of multiple trees, which makes a post hoc removal of features infeasible. Feature selection methods therefore often either focus on simple pre-filtering methods, or require many Random Forest evaluations along their optimization path, which drastically increases the computational complexity. To solve both issues, we propose Shallow Tree Selection, a novel fast and multivariate feature selection method that selects features from small tree structures. Additionally, we also adapt three standard feature selection algorithms for cost-sensitive learning by introducing a hyperparameter-controlled benefit-cost ratio criterion (BCR) for each method. In an extensive simulation study, we assess this criterion, and compare the proposed methods to multiple performance-based baseline alternatives on four artificial data settings and seven real-world data settings. We show that all methods using a hyperparameterized BCR criterion outperform the baseline alternatives. In a direct comparison between the proposed methods, each method indicates strengths in certain settings, but no one-fits-all solution exists. On a global average, we could identify preferable choices among our BCR based methods. Nevertheless, we conclude that a practical analysis should never rely on a single method only, but always compare different approaches to obtain the best results.