  A new concept of moderate non-locality in higher-spin gauge theory is
introduced. Based on the recently proposed differential homotopy approach, a
moderately non-local scheme, that issofter than those resulting from the
shifted homotopy approach available in the literature so far, is worked out in
the mixed $\eta\bar\eta$ sector of the Vasiliev higher-spin theory. To
calculate moderately non-local vertices $\Upsilon^{\eta\bar \eta}(\omega,
C,C,C)$ for all ordering of the fields $\omega$ and $C$ we apply an
interpolating homotopy, that respects the moderate non-locality in the
perturbative analysis of the higher-spin equations.
