Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still require prohibitive computational costs. We propose a family of algorithms which split the classification task into two stages: representation learning and uncertainty estimation. We compare four specific instances, where uncertainty estimation is performed via either an ensemble of Stochastic Gradient Descent or Stochastic Gradient Langevin Dynamics snapshots, an ensemble of bootstrapped logistic regressions, or via a number of Monte Carlo Dropout passes. We evaluate their performance in terms of \emph{selective} classification (risk-coverage), and their ability to detect out-of-distribution samples. Our experiments suggest there is limited value in adding multiple uncertainty layers to deep classifiers, and we observe that these simple methods strongly outperform a vanilla point-estimate SGD in some complex benchmarks like ImageNet.