  We prove that there exists a>0 such that for any integer d>2 and any
topological types S_1,...,S_n of plane curve singularities, satisfying
$\mu(S_1)+...+\mu(S_n) \leq ad^2$, there exists a reduced irreducible plane
curve of degree d with exactly n singular points of types S_1,...,S_n,
respectively. This estimate is optimal with respect to the exponent of d. In
particular, we prove that for any topological type S there exists an
irreducible polynomial of degree $d \leq 14\sqrt{\mu(S)}$ having a singular
point of type S.
