The Basic Formal Ontology (BFO) class continuant fiat boundary and its subclasses, including fiat surface, are not heavily axiomatized; they have elucidations, not definitions; and the meanings of these elucidations are poorly captured by the relevant BFO axioms. This paper is an effort to make progress in these respects for fiat surface. We identify a range of desiderata for a BFO-conformant view of fiat surface, argue that the GitHub does not satisfy them, argue that the view of fiat surfaces in Arp et al. (2015) does a better job, and supplement that view in ways that do a still better job. Our discussion allows us to, inter alia, present a number of axioms relevant to our topic worthy of consideration for inclusion in BFO or dependent ontologies in specific domains and for specific purposes.