  We show that every smooth projective curve over a finite field k admits a
finite tame morphism to the projective line over k. Furthermore, we construct a
curve with no such map when k is an infinite perfect field of characteristic
two. Our work leads to a refinement of the tame Belyi theorem in positive
characteristic, building on results of Sa\"idi, Sugiyama-Yasuda, and
Anbar-Tutdere.
