  A space has $\sigma$-compact tightness if the closures of $\sigma$-compact
subsets determines the topology. We consider a dense set variant that we call
densely k-separable. We consider the question of whether every densely
k-separable space is separable. The somewhat surprising answer is that this
property, for compact spaces, implies that every dense set is separable. The
path to this result relies on the known connections established between
$\pi$-weight and the density of all dense subsets, or more precisely, the
cardinal invariant $\delta(X)$.
