  We define a weak iterability notion that is sufficient for a number of
arguments concerning $\Sigma_1$-definability at uncountable regular cardinals.
In particular we give its exact consistency strength firstly in terms of the
second uniform indiscernible for bounded subsets of $\kappa$: $u_2(\kappa)$,
and secondly to give the consistency strength of a property of L\"ucke's.
  Theorem: The following are equiconsistent:
  (i) There exists $\kappa$ which is stably measurable;
  (ii) for some cardinal $\kappa$, $u_2(\kappa)=\sigma(\kappa)$;
  (iii) The {\boldmath $\Sigma_1$}-club property holds at a cardinal $\kappa$.
  Here $\sigma(\kappa)$ is the height of the smallest $M \prec_{\Sigma_1}
H(\kappa^+)$ containing $\kappa+1$ and all of $H(\kappa)$.
