  Intrinsic tame filling functions are quasi-isometry invariants that are
refinements of the intrinsic diameter function of a group. The main purpose of
this paper is to show that every finite presentation of a group has an
intrinsic tame filling function that is equivalent to its intrinsic diameter
function. We also introduce some alternative filling functions--based on
concepts similar to those used to define intrinsic tame filling functions--that
are potential proper refinements of the intrinsic diameter function.
