  This paper addresses an issue essential to the study of hidden
supersymmetries (meaning here ones that do not close on the Hamiltonian) for
one-dimensional non-linear supersymmetric sigma models. The issue relates to
ambiguities, due to partial integrations in superspace, both in the actual
definition of these supersymmetries and in the Noether definition of the
associated supercharges. The unique consistent forms of both these definitions
have to be determined simultaneously by a process that adjusts the former
definitions so that the associated supercharges do indeed correctly generate
them with the aid of the canonical formalism. The paper explains and
illustrates these matters and gives some new results.
