For every fixed-point expression e of alternation-depth r,
we construct a new fixed-point expression e' of alternation-depth 2
and size ${\cal O}(r\cdot|e|)$. Expression e' is equivalent to e
whenever operators are distributive and the underlying
complete lattice has a co-continuous least upper bound. We
alternation-depth but also w.r.t. the increase in size of the
resulting expression.