Disulfide bridges strongly constrain the native structure of many proteins and predicting their formation is therefore a key sub-problem of protein structure and function inference. Most recently proposed approaches for this prediction problem adopt the following pipeline: first they enrich the primary sequence with structural annotations, second they apply a binary classifier to each candidate pair of cysteines to predict disulfide bonding probabilities and finally, they use a maximum weight graph matching algorithm to derive the predicted disulfide connectivity pattern of a protein. In this paper, we adopt this three step pipeline and propose an extensive study of the relevance of various structural annotations and feature encodings. In particular, we consider five kinds of structural annotations, among which three are novel in the context of disulfide bridge prediction. So as to be usable by machine learning algorithms, these annotations must be encoded into features. For this purpose, we propose four different feature encodings based on local windows and on different kinds of histograms. The combination of structural annotations with these possible encodings leads to a large number of possible feature functions. In order to identify a minimal subset of relevant feature functions among those, we propose an efficient and interpretable feature function selection scheme, designed so as to avoid any form of overfitting. We apply this scheme on top of three supervised learning algorithms: k-nearest neighbors, support vector machines and extremely randomized trees. Our results indicate that the use of only the PSSM (position-specific scoring matrix) together with the CSP (cysteine separation profile) are sufficient to construct a high performance disulfide pattern predictor and that extremely randomized trees reach a disulfide pattern prediction accuracy of on the benchmark dataset SPX, which corresponds to improvement over the state of the art. A web-application is available at http://m24.giga.ulg.ac.be:81/x3CysBridges.