  We obtain results on the condensation principle called local club
condensation. We prove that in extender models an equivalence between the
failure of local club condensation and subcompact cardinals holds. This gives a
characterization of $\square_{\kappa}$ in terms of local club condensation in
extender models. Assuming $\gch$, given an interval of ordinals $I$ we verify
that iterating the forcing defined by Holy-Welch-Wu, we can preserve $\gch$,
cardinals and cofinalities and obtain a model where local club condensation
holds for every ordinal in $I$ modulo those ordinals which cardinality is a
singular cardinal.
  We prove that if $\kappa$ is a regular cardinal in an interval $I$, the above
iteration provides enough condensation for the combinatorial principle
$\Dl_{S}^{*}(\Pi^{1}_{2})$, and in particular $\diamondsuit(S)$, to hold for
any stationary $S \subseteq \kappa$.
