  Let C be a 2-connected Gorenstein curve either reduced or contained in a
smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim
scheme such that the space H^0(C, I_S K_C) contains a generically invertible
section). Under some general assumptions on S or C we show that h^0(C, I_S K_C)
<= p_a(C) - deg (S)/2 and if equality holds then either S is trivial, or C is
honestly hyperelliptic or 3-disconnected. As a corollary we give a
generalization of Clifford's theorem for reduced curves.
