The condition has been formulated for barrierless vapor condensation to proceed on soluble nuclei over the range of incomplete nucleus dissolution at all values of the vapor chemical potential which allow barrierless condensation over the range of complete nucleus dissolution. For the condition formulated, a sufficient limitation on nucleus solubility from below has been found for molecular as well as nonionic and ionic micellar solution inside arising droplet. It has been shown that the limitation really holds at such large nucleus sizes which are needed for applicability of the limitation and, at the same time, are most interesting in practice, and at which condensation is possible at low vapor supersaturations. The limitation found is general and is not bounded by the specific form of the disjoining pressure isotherms and specific mechanism of wetting of condensation nucleus.