  We show that the stable and unstable sets of non-uniformly hyperbolic
horseshoes arising in some heteroclinic bifurcations of surface diffeomorphisms
have the value conjectured in a previous work by the second and third authors
of the present paper. Our results apply to first heteroclinic bifurcations
associated to horseshoes with Hausdorff dimension $<22/21$ of conservative
surface diffeomorphisms.
