  A $p$-divisible group over a field $K$ admits a slope decomposition;
associated to each slope $\lambda$ is an integer $m$ and a representation
$\gal(K) \ra \gl_m(D_\lambda)$, where $D_\lambda$ is the $\rat_p$-division
algebra with Brauer invariant $[\lambda]$. We call $m$ the multiplicity of
$\lambda$ in the $p$-divisible group. Let $G_0$ be a $p$-divisible group over a
field $k$. Suppose that $\lambda$ is not a slope of $G_0$, but that there
exists a deformation of $G$ in which $\lambda$ appears with multiplicity one.
Assume that $\lambda\not= (s-1)/s$ for any natural number $s>1$. We show that
there exists a deformation $G/R$ of $G_0/k$ such that the representation
$\gal(\Frac R) \ra \gl_1(D_\lambda)$ has large image.
