  We discuss to what extent certain results about totally ramified values of
entire and meromorphic functions remain valid if one relaxes the hypothesis
that some value is totally ramified by assuming only that all islands over some
Jordan domain are multiple. In particular, we prove a result suggested by Bloch
which says that an entire function of order less than $1$ has a simple island
over at least one of two given Jordan domains with disjoint closures.
