Despite the empirical success of knowledge distillation, current state-of-the-art methods are computationally expensive to train, which makes them difficult to adopt in practice. To address this problem, we introduce two distinct complementary losses inspired by a cheap entropy-like estimator. These losses aim to maximise the correlation and mutual information between the student and teacher representations. Our method incurs significantly less training overheads than other approaches and achieves competitive performance to the state-of-the-art on the knowledge distillation and cross-model transfer tasks. We further demonstrate the effectiveness of our method on a binary distillation task, whereby it leads to a new state-of-the-art for binary quantisation and approaches the performance of a full precision model. Code: www.github.com/roymiles/ITRD