We study a set of various tree-like classifiers, from single CART trees to bagging and boosting ensembles of individual decision trees, applied to wavelet features of dermoscopy images for the sake of computer-aided diagnosis (CAD) of melanoma, the cancer of pigment cells in the skin. The goal of this feature extraction task is, first, to seek for the best hyperparameters of the models involved, and, second, to extract the best, robust features that are best prepared for a variety of image resolutions. We show AUC (area under the ROC curve) of the tree-like classifiers for a data set ISIC 2017 and optimized with Bayesian search as a function of the wavelet base. The most efficient wavelet bases include biorthogonal and reverse biorthogonal wavelet families. The most efficient and resolution-robust wavelet is Rbio3.1. The absolute values of AUC reach, respectively, 77-88%, 85%, and 90%, for the CART trees grown by the Gini splitting criterion and prunned optimally, for the bagging ensembles, and for the boosting ensembles trained with TotalBoost.