A new class of semi-mixed effects models is introduced. It includes random or mixed and fixed effects models as extreme cases. In multi-level regression, such as small area studies, and in panel data studies, using a fixed effect for each region leads to models that are flexible but that have poor estimation accuracy; they are over-parameterized. Regarding region as a random effect reduces the number of parameters, and hence the flexibility, but needs crucial assumptions, such as that of independence between covariates and the random effects. The proposed class of models constitutes a continuum of models, indexed by a "slider", that determines the position of the model between these two extremes. So one can choose a model that is close to the parsimonious random effects case, but far enough away from it to filter out unwanted dependencies. The methodology is used for a small area analysis of tourist expenditures in Galicia.