In a previous paper, we described a natural closed subset,
M
0
1,k(X,A; J), of the moduli space M1,k(X,A; J) of stable genusone
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
and conclude that M
0
1,k(X,A; J), just like M1,k(X,A; J), carries
a virtual fundamental class, which 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 M1,k(X,A; J). 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.