  This paper adresses two issues in dealing with bicategories of fractions. The
first is to introduce a set of conditions on a class of arrows in a bicategory
which is weaker than the one given in Pronk, Etendues and stacks as
bicategories of fractions, but still allows a bicalculus of fractions. These
conditions allow us to invert a smaller collection of arrows so that in some
cases we may obtain a bicategory of fractions with small hom-categories. We
adapt the construction of the bicategory of fractions to work with the weaker
conditions. The second issue is the difficulty in dealing with 2-cells, which
are defined by equivalence classes. We discuss conditions under which there are
canonical representatives for 2-cells, and how pasting of 2-cells can be
simplified in the presence of certain pseudo pullbacks. We also discuss how
both of these improvements apply in the category of orbispaces.
