  Let $O_D$ be the ring of integers in a division algebra of invariant $1/n$
over a p-adic local field. Drinfeld proved that the moduli problem of special
formal $O_D$-modules is representable by Deligne's formal scheme version of the
Drinfeld p-adic halfspace. In this paper we exhibit other moduli spaces of
formal $p$-divisible groups which are represented by $p$-adic formal schemes
whose generic fibers are isomorphic to the Drinfeld p-adic halfspace. We also
prove an analogue concerning the Lubin-Tate moduli space.
