We review a number of multi-population mortality models: variations of the Li and Lee (2005) model, and the common-age-effect (CAE) model of Kleinow (2014). Model parameters are estimated using maximum likelihood. Although this introduces some challenging identifiability problems and complicates the estimation process it allows a fair comparison of the different models. We propose to solve these identifiability problems by applying two dimensional constraints over the parameters. Using data from six countries, we compare and rank, both visually and numerically, the models' fitting qualities and develop forecasting models that produce nondiverging, joint mortality rate scenarios.It is found that the CAE model fits best. But we also find that the Li and Lee model potentially suffers from robustness problems when calibrated using maximum likelihood.