  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 $(m,\Omega,\Omega+1)^*$-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 $M^{\vec{\mathcal{T}}}_\infty=M^{\mathcal{X}}_\infty$, along with
agreement of iteration maps when there are no drops in model or degree on main
branches. We also use the methods to analyze the comparison of multiple
iterates via such a common strategy.
