  Let $p$ and $\ell$ be distinct primes, and $\rho$ be an orthogonal or
symplectic representation of the absolute Galois group of an $\ell$-adic field
over a finite field of characteristic $p$. We define and study a liftable
deformation condition of lifts of $\rho$ "ramified no worse than $\rho$",
generalizing the minimally ramified deformation condition for $GL_n$ studied in
\cite{cht08}. The key insight is to restrict to deformations where an
associated unipotent element does not change type when deforming. This requires
an understanding of nilpotent orbits and centralizers of nilpotent elements in
the relative situation, not just over fields.
