  In a previous paper we described a natural closed subset of the moduli space
of stable genus-one J-holomorphic maps into a symplectic manifold X. In this
paper we generalize the definition of the main component to moduli spaces of
perturbed, in a restricted way, J-holomorphic maps. This generalization implies
that the main component, just like the entire moduli space, carries a virtual
fundamental class and can be used to define symplectic invariants. These truly
genus-one invariants constitute part of the standard genus-one Gromov-Witten
invariants, which arise from the entire moduli space. The new invariants are
more geometric and can be used to compute the genus-one GW-invariants of
complete intersections, as shown in a separate paper.
