  It was recently proved that embedded solutions of Euclidean hypersurface
flows with speeds given by concave (convex), degree one homogeneous functions
of the Weingarten map are interior (exterior) non-collapsing. These results
were subsequently extended to hypersurface flows in the sphere and hyperbolic
space.
  In the first part of the paper, we show that locally convex solutions are
exterior non-collapsing for a larger class of speed functions than previously
considered; more precisely, we show that the previous results hold when
convexity of the speed function is relaxed to inverse-concavity. We note that
inverse-concavity is satisfied by a large class of concave speed functions. As
a consequence, we obtain a large class of two-sided non-collapsing flows,
whereas previously two-sided non-collapsing was only known for the mean
curvature flow.
  In the second part of the paper, we demonstrate the utility of two sided
non-collapsing with a straightforward proof of convergence of compact, convex
hypersurfaces to round points.
  The proof of the non-collapsing estimate is similar to the previous results
mentioned, in that we show that the exterior ball curvature is a viscosity
supersolution of the linearised flow. The new ingredient is the following
observation: Since the function which provides an upper support in the
derivation of the viscosity inequality is defined on $M\times M$ (or $TM$ in
the `boundary case'), whereas the exterior ball curvature and the linearised
flow equation depend only on the first factor, we are privileged with a freedom
of choice in which second derivatives from the extra directions to include in
the calculation. The optimal choice is closely related to the class of
inverse-concave speed functions.
