Significant advances have been made in Natural Language Processing (NLP) modelling since the beginning of 2018. The new approaches allow for accurate results, even when there is little labelled data, because these NLP models can benefit from training on both task-agnostic and task-specific unlabelled data. However, these advantages come with significant size and computational costs. This workshop paper outlines how our proposed convolutional student architecture, having been trained by a distillation process from a large-scale model, can achieve 300x inference speedup and 39x reduction in parameter count. In some cases, the student model performance surpasses its teacher on the studied tasks.