Let $\alpha$ be any countable admissible ordinal greater than $\omega$. There is a transitive set $A$ such that $A$ is admissible, locally countable, $On^A = \alpha$, and $A$ satisfies $\Sigma_1$-separation. In fact, if $B$ is any nonstandard model of $KP + \forall x \subseteq \omega$ (the hyperjump of $x$ exists), the ordinal standard part of $B$ is greater than $\omega$, and every standard ordinal in $B$ is countable in $B$, then $HC^B \cap$ (standard part of $B$) satisfies $\Sigma_1$-separation.