Coresets are compact representations of datasets such that models trained on a coreset are provably competitive with models trained on the full data set. As such, they have been successfully used to scale up clustering models to massive data sets. While existing approaches generally only allow for multiplicative approximation errors, we propose a novel notion of lightweight coresets that allows for both multiplicative and additive errors. We provide a single algorithm to construct lightweight coresets for k-Means clustering as well as soft and hard Bregman clustering. The algorithm is substantially faster than existing constructions, embarrassingly parallel and the resulting coresets are smaller. We demonstrate that the proposed method outperforms existing coreset constructions in practice.