  In this paper we consider a family of active scalars with a velocity field
given by $u = \Lambda^{-1+\alpha}\nabla^{\perp} \theta$, for $\alpha \in
(0,1)$. This family of equations is a more singular version of the
two-dimensional Surface Quasi-Geostrophic (SQG) equation, which would
correspond to $\alpha=0$.
  We consider the evolution of sharp fronts by studying families of
almost-sharp fronts. These are smooth solutions with simple geometry in which a
sharp transition in the solution occurs in a tubular neighbourhood (of size
$\delta$). We study their evolution and that of compatible curves, and
introduce the notion of a spine for which we obtain improved evolution results,
gaining a full power (of $\delta$) compared to other compatible curves.
