Hunt showed that the notion of PER-based strictness properties subsumed the incomparable notions of ideal- and projection-based properties on non-lifted value spaces. We extend Hunt's idea so it can encompass other comportment properties (such as totality) by separating the information and fixpoint orderings. We then define a class of uniform PERs (in the sense that they treat non-bottom ground elements, e.g. integers, identically) and then show how these can be hereditarily defined on function spaces. These (or subsets thereof) can be taken as a space of abstract values for abstract interpretation in the style of Nielson.