  We study the approximability of instances of the minimum entropy set cover
problem, parameterized by the average frequency of a random element in the
covering sets. We analyze an algorithm combining a greedy approach with another
one biased towards large sets. The algorithm is controled by the percentage of
elements to which we apply the biased approach. The optimal parameter choice
has a phase transition around average density $e$ and leads to improved
approximation guarantees when average element frequency is less than $e$.
