We propose novel neural temporal models for short-term motion prediction and long-term human motion synthesis, achieving state-of-art predictive performance while being computationally less expensive compared to previously proposed approaches. Key aspects of our proposed system include: 1) a novel, two-level processing architecture that aids in generating planned trajectories, 2) a simple set of easily computable features that integrate simple derivative information into the model, and 3) a novel multi-objective loss function that helps the model to slowly progress from the simpler task of next-step prediction to the harder task of multi-step closed-loop prediction. Our results demonstrate that these innovations are shown to facilitate improved modeling of long-term motion trajectories. Finally, we propose a novel metric called Power Spectrum Similarity (NPSS) to evaluate the long-term predictive ability of our trained motion synthesis models, circumventing many of the shortcomings of the popular mean-squared error measure of the Euler angles of joints over time.