In binary response models, it may happen that iterative parameter estimation diverges because binary outcomes are perfectly predictable for some or all subjects. However, in contrast to what data analysis might suggest, we assume that the measured covariates are not sufficient to predict the outcome status perfectly. This phenomenon, termed 'separation', is rather considered a small-sample problem. Firth's correction to logistic regression has become a standard procedure to deal with separation in binary response models with fixed effects. We will first review Firth's and other methods to deal with separation (Mansournia, Geroldinger, Greenland, Heinze, Am J Epi 2018). For random effects models, satisfactory paralleling solutions have been repeatedly called for, but are still missing in the statistical literature. In this presentation we would like to share some of our ideas on how to tackle the problem. We will first define desirable properties of possible solutions. Then, starting at the abovementioned approaches, we will explore some suitable extensions for mixed models. In particular, Bayesian approaches, solutions based on ridge regression and data augmentation could be promising candidates to address the problem. A colonoscopy study comparing purgatives for bowel preparation will serve as an illustrative example.