In an earlier paper [Trans. Am. Math. Soc. 355, No. 9, 3485–3512 (2003; Zbl 1032.14005)], the author gave sufficient conditions for the irreducibility of the family \(V^{\text{irr}}\) of irreducible curves which have prescribed arbitrary singularities and belong to a given linear system on smooth projective surfaces \(S\) of several types. The conditions were expressed in the form of an upper bound on the sum of certain singularity invariants by \(\gamma (D-K_{S})^2\), where \(K_{S}\) is the canonical divisor of \(S\) and \(\gamma\) is some constant. In the present paper the author improves this condition, that is the constant \(\gamma\), by a factor of \(9\). The proof proceeds along the same lines of the original one, by showing that some irreducible “regular” subscheme of \(V^{\text{irr}}\) is dense in \(V^{\text{irr}}\), following the approach contained in an unpublished paper of G. M. Greuel, C. Lossen and E. Shustin [“On the irreducibility of families of curves” (1998)], which is based on ideas of L. Chiantini and C. Ciliberto [J. Algebr. Geom. 8, No. 1, 67–83 (1999; Zbl 0973.14017)].