Deep neural networks (DNNs) have recently been the focus of much text-to-speech research as a replacement for decision trees and hidden Markov models (HMMs) in statistical parametric synthesis systems. Performance improvements have been reported; however, the configuration of systems evaluated makes it impossible to judge how much of the improvement is due to the new machine learning methods, and how much is due to other novel aspects of the systems. Specifically, whereas the decision trees in HMM-based systems typically operate at the state-level, and separate trees are used to handle separate acoustic streams, most DNN-based systems are trained to make predictions simultaneously for all streams at the level of the acoustic frame. This paper isolates the influence of three factors (machine learning method; state vs. frame predictions; separate vs. combined stream predictions) by building a continuum of systems along which only a single factor is varied at a time. We find that replacing decision trees with DNNs and moving from state-level to frame-level predictions both significantly improve listeners' naturalness ratings of synthetic speech produced by the systems. No improvement is found to result from switching from separate-stream to combined-stream predictions.