Intuition suggests, to most people, that parents should be selected to care for their offspring in relation to how certain they are of being the parents of those offspring. Theoretical models of the relationship between parental investment and certainty of parentage predict the two to be related only when some other assumptions are made, few of which can be taken for granted. I briefly review the models and their assumptions, and discuss two kinds of difficulty facing an empiricist wishing to test the models. The first is the problem of unmeasured (and immeasurable) variables. The second is the problem that even the most extensive models do not capture the complexity that can be demonstrated in real systems. I illustrate some of these problems, and some qualitative tests of the models, with experimental work on a population of the collared flycatcher. My conclusion is that although there are some cases where the models have qualitative support, we are a long way from understanding whether paternal care is commonly adjusted in relation to certainty of paternity.