  We consider a broad class of consistently reduced Manin-Radul supersymmetric
KP hierarchies (MR-SKP) which are supersymmetric analogs of the ordinary
bosonic constrained KP models. Compatibility of these reductions with the MR
fermionic isospectral flows is achieved via appropriate modification of the
latter preserving their (anti-)commutation algebra. Unlike the general
unconstrained MR-SKP case, Darboux-Backlund transformations do preserve the
fermionic isospectral flows of the reduced MR-SKP hierarchies. This allows for
a systematic derivation of explicit Berezinian solutions for the
super-tau-functions (super-solitons) for these models.
