  The number of Morse points in a Morsification determines the topology of the
Milnor fibre of a holomorphic function germ $f$ with isolated singularity. If
$f$ has an arbitrary singular locus, then this nice relation to the Milnor
fibre disappears. We show that despite this loss, the numbers of stratified
Morse singularities of a general linear Morsification are effectively
computable in terms of topological invariants of $f$.
