  We continue the work done by Gitik, Kanovei, Koepke, and later by the
authors. We prove that for every set $A$ in a Magidor-Radin generic extension
using a coherent sequence such that $o^{\vec{U}}(\kappa)<\kappa$, there is a
subset $C'$ of the Magidor club such that $V[A]=V[C']$. Also we classify all
intermediate $ZFC$ transitive models $V\subseteq M\subseteq V[G]$.
