  We construct $O(1)\times O(n)$-invariant ancient ``pancake'' solutions to a
large and natural class of fully nonlinear curvature flows. We then establish
that these are the unique $O(n)$-invariant ancient solutions to the
corresponding flow which sweep out a slab by carrying out a fine asymptotic
analysis for this class. This extends the main results of \cite{BLT} to a
surprisingly general class of flows.
