Discriminating between Similar Languages (DSL) is a challenging task addressed at the VarDial Workshop series. We report on our participation in the DSL shared task with a two-stage system. In the first stage, character n-grams are used to separate language groups, then specialized classifiers distinguish similar language varieties. We have conducted experiments with three system configurations and submitted one run for each. Our main approach is a word-level convolutional neural network (CNN) that learns task-specific vectors with minimal text preprocessing. We also experiment with multi-layer perceptron (MLP) networks and another hybrid configuration. Our best run achieved an accuracy of 90.76%, ranking 8th among 11 participants and getting very close to the system that ranked first (less than 2 points). Even though the CNN model could not achieve the best results, it still makes a viable approach to discriminating between similar languages.