Recently, multiple systems estimation (MSE) has been applied to estimate the number of victims of human trafficking in different countries. The estimation procedure consists of a log-linear analysis of a contingency table of population registers and covariates. As the number of potential models increases exponentially with the number of registers and covariates, it is practically impossible to fit and compare all models. Therefore, the model search needs to be restricted to a small subset of all potential models. This paper addresses principles and criteria for model assessment and selection for MSE of human trafficking with special attention to sparsity which is typical to human trafficking data. The concepts are illustrated on data from Slovakia and Romania.