Label shift refers to the phenomenon where the prior class probability p(y) changes between the training and test distributions, while the conditional probability p(x|y) stays fixed. Label shift arises in settings like medical diagnosis, where a classifier trained to predict disease given symptoms must be adapted to scenarios where the baseline prevalence of the disease is different. Given estimates of p(y|x) from a predictive model, Saerens et al. proposed an efficient EM algorithm to correct for label shift that does not require model retraining. A limiting assumption of this algorithm is that p(y|x) is calibrated, which is not true of modern neural networks. Recently, Black Box Shift Learning (BBSL) and Regularized Learning under Label Shifts (RLLS) have emerged as state-of-the-art techniques to cope with label shift when a classifier does not output calibrated probabilities. However, both BBSL and RLLS require model retraining with importance weights, which poses challenges in practice, and neither has been benchmarked against EM. We show that by combining EM with a type of calibration we call bias-corrected calibration, we outperform both BBSL and RLLS across diverse datasets and distribution shifts. We further show that the EM objective is concave and bounded, and introduce a theoretically principled strategy for estimating source-domain priors that improves robustness to poor calibration. This work demonstrates that EM with appropriate calibration is a formidable and efficient baseline that future work in label shift adaptation should be compared with. Colab notebooks reproducing experiments are available at (anonymized link): https://github.com/blindauth/labelshiftexperiments