We investigate the utility of a variety of features in performing morphological galaxy classification using back-propagation neural network classifiers based on a sample of 805 galaxies classified by Naim et al. We derive a total of 22 features from each galaxy image and use these as inputs to a neural network trained using back-propagation. The morphological types are subdivided into two to seven groups, and the relevance of each of the features is examined for each grouping. We use the magnitude of the regularization parameter for each input to determine whether a feature can be eliminated. We then prune the input features of the network, typically down to four features. We examine a number of methods of assessing the performance of the network and determine which works best for our task.