  In recently published work Maskit constructs a fundamental domain D_g for the
Teichmueller modular group of a closed surface S of genus g>1. Maskit's
technique is to demand that a certain set of 2g non-dividing geodesics C_{2g}
on S satisfies certain shortness criteria. This gives an a priori infinite set
of length inequalities that the geodesics in C_{2g} must satisfy. Maskit shows
that this set of inequalities is finite and that for genus g=2 there are at
most 45. In this paper we improve this number to 27. Each of these
inequalities: compares distances between Weierstrass points in the fundamental
domain S-C_4 for S; and is realised (as an equality) on one or other of two
special surfaces.
