We explore the consequences of the Higgs fields acting as messengers of
supersymmetry breaking. The hidden-sector paradigm in the gauge mediation
framework is relaxed by allowing two types of gauge-invariant, renormalizable
operators that are typically discarded: direct coupling between the Higgses and
supersymmetry breaking singlets, and Higgs-messenger mixing terms. The most
important phenomenological consequence is a flavor-dependent shift in sfermion
masses. This is from a one-loop contribution, which we compute for a general
set of weak doublet messengers. We also study a couple of explicit models in
detail, finding that precision electroweak constraints can be satisfied with a
spectrum significantly different from that of gauge mediation.Comment: 20 pages, 5 figure