  Given a limit sketch in which the cones have a finite connected base, we show
that a model structure of "up to homotopy" models for this limit sketch in a
suitable model category can be transferred to a Quillen equivalent model
structure on the category of strict models. As a corollary of our general
result, we obtain a rigidification theorem which asserts in particular that any
$\Theta_n$-space in the sense of Rezk is levelwise equivalent to one that
satisfies the Segal conditions on the nose. There are similar results for
dendroidal spaces and $n$-fold Segal spaces.
