  We revisit several results concerning club principles and nonsaturation of
the nonstationary ideal, attempting to improve them in various ways. So we
typically deal with a (non necessarily normal) ideal $J$ extending the
nonstationary ideal on a regular uncountable (non necessarily successor)
cardinal $\kappa$, our goal being to witness the nonsaturation of $J$ by the
existence of towers (of length possibly greater than $\kappa^+$).
