A subset $D$ is a discretely dense subset of a space $X$ if every point of $X$ is in the closure of a discrete subset of $D$. The cardinal invariant, $Dd(X)$, was introduced by Juhasz and is the minimum cardinality of a discretely dense subset of $X$. We are reporting on some recent work with Juhasz and van Mill on results that improve upon the, seemingly only, obvious inequalities $d(X)\le Dd(X)\le |X|$. We also consider, $Fd(X)$, the free sequence density number.