A result of Beckmann says that for any 3-point G-Galois cover of the Riemann sphere, if a prime p does not divide the order of G, then p is unramified in the field of moduli of the G-cover. Wewers generalized this: if p exactly divides the order of G, then p is at worst tamely ramified in the field of moduli. We will discuss extensions of this result, contained in the speaker's thesis, involving more general groups G with cyclic p-Sylow groups.