I show that the set of smooth curves of genus g admitting branched coverings
X->P^1 with only triple ramification points has dimension at least max(2g-3,g).
In characteristic two, such curves have tame rational functions and an analog
of Belyi's Theorem applies to them.Comment: 12 pages, section on semistable reduction extended, otherwise minor
changes, to appear in Ann. Inst. Fourie
