  In statistical applications, the normal and the Laplace distributions are
often contrasted: the former as a standard tool of analysis, the latter as its
robust counterpart. I discuss the convolutions of these two popular
distributions and their applications in research. I consider four models within
a simple $2\times 2$ scheme which is of practical interest in the analysis of
clustered (e.g., longitudinal) data. In my view, these models, some of which
are less known than others by the majority of applied researchers, constitute a
'family' of sensible alternatives when modelling issues arise. In three
examples, I revisit data published recently in the epidemiological and clinical
literature as well as a classic biological dataset.
