Deep neural networks lack interpretability and tend to be overconfident, which poses a serious problem in safety-critical applications like autonomous driving, medical imaging, or machine vision tasks with high demands on reliability. Quantifying the predictive uncertainty is a promising endeavour to open up the use of deep neural networks for such applications. Unfortunately, current available methods are computationally expensive. In this work, we present a novel approach for efficient and reliable uncertainty estimation which we call Deep Uncertainty Distillation using Ensembles for Segmentation (DUDES). DUDES applies student-teacher distillation with a Deep Ensemble to accurately approximate predictive uncertainties with a single forward pass while maintaining simplicity and adaptability. Experimentally, DUDES accurately captures predictive uncertainties without sacrificing performance on the segmentation task and indicates impressive capabilities of identifying wrongly classified pixels and out-of-domain samples on the Cityscapes dataset. With DUDES, we manage to simultaneously simplify and outperform previous work on Deep Ensemble-based Uncertainty Distillation.