Speech emotion recognition (SER) is the task of recognising humans' emotional states from speech. SER is extremely prevalent in helping dialogue systems to truly understand our emotions and become a trustworthy human conversational partner. Due to the lengthy nature of speech, SER also suffers from the lack of abundant labelled data for powerful models like deep neural networks. Pre-trained complex models on large-scale speech datasets have been successfully applied to SER via transfer learning. However, fine-tuning complex models still requires large memory space and results in low inference efficiency. In this paper, we argue achieving a fast yet effective SER is possible with self-distillation, a method of simultaneously fine-tuning a pretrained model and training shallower versions of itself. The benefits of our self-distillation framework are threefold: (1) the adoption of self-distillation method upon the acoustic modality breaks through the limited ground-truth of speech data, and outperforms the existing models' performance on an SER dataset; (2) executing powerful models at different depths can achieve adaptive accuracy-efficiency trade-offs on resource-limited edge devices; (3) a new fine-tuning process rather than training from scratch for self-distillation leads to faster learning time and the state-of-the-art accuracy on data with small quantities of label information.