We introduce the fully automatic design of a numerically optimized decision-tree algorithm and demonstrate its application to sea ice classification from SAR data. In the decision tree, an initial multi-class classification problem is split up into a sequence of binary problems. Each branch of the tree separates one single class from all other remaining classes, using a class-specific selected feature set. We optimize the order of classification steps and the feature sets by combining classification accuracy and sequential search algorithms, looping over all remaining features in each branch. The proposed strategy can be adapted to different types of classifiers and measures for the class separability. In this study, we use a Bayesian classifier with non-parametric kernel density estimation of the probability density functions. We test our algorithm on simulated data as well as airborne and spaceborne SAR data over sea ice. For the simulated cases, average per-class classification accuracy is improved between 0.5% and 4% compared to traditional all-at-once classification. Classification accuracy for the airborne and spaceborne SAR datasets was improved by 2.5% and 1%, respectively. In all cases, individual classes can show larger improvements up to 8%. Furthermore, the selection of individual feature sets for each single class can provide additional insights into physical interpretation of different features. The improvement in classification results comes at the cost of longer computation time, in particular during the design and training stage. The final choice of the optimal algorithm therefore depends on time constraints and application purpose.