  We describe the extension of normal iteration strategies with appropriate
condensation properties to strategies for stacks of normal trees, with full
normalization. Given a regular uncountable cardinal $\Omega$ and an
$(m,\Omega+1)$-iteration strategy $\Sigma$ for a premouse $M$, such that
$\Sigma$ and $M$ both have appropriate condensation properties, we extend
$\Sigma$ to a strategy $\Sigma^*$ for the
optimal-$(m,\Omega,\Omega+1)^*$-iteration game such that for all
$\lambda<\Omega$ and all stacks
$\vec{\mathcal{T}}=\left<\mathcal{T}_\alpha\right>_{\alpha<\lambda}$ via
$\Sigma^*$, consisting of normal trees $\mathcal{T}_\alpha$, each of length
${<\Omega}$, there is a corresponding normal tree $\mathcal{X}$ via $\Sigma$
with $M^{\vec{\mathcal{T}}}_\infty=M^{\mathcal{X}}_\infty$. Moreover, if there
are no drops in model or degree along the main branches of these trees then the
overall iteration maps $i^{\vec{\mathcal{T}}}:M\to
M^{\vec{\mathcal{T}}}_\infty$ and $i^{\mathcal{X}}:M\to M^{\mathcal{X}}_\infty$
agree. The construction is the result of a combination of work of John Steel
and of the author.
  We also establish some further useful properties of $\Sigma^*$, and use the
methods to analyze the comparison of multiple iterates via a common such
strategy.
