  We study the notion of tightly stationary sets which was introduced by
Foreman and Magidor in \cite{ForMag-MS}. We obtain two consistency results
which show that it is possible for a sequence of regular cardinals $( \kappa_n
)_{n < \omega}$ to have the property that for every sequence $\vec{S}$, of some
fixed-cofinality stationary sets $S_n \subseteq \kappa_n$, $\vec{S}$ is tightly
stationary in a generic extension. The results are obtained using variations of
the short-extenders forcing method.
