projective $3$-fold $X$ is never ideal in this sense, but one might hope that $X$ becomes ideal if its Kahler complex structure is replaced with a generic almost complex one. We show that this is indeed the case in the “Fano" case.\
If $(X,\om)$ is a compact symplectic manifold, $g\!\in\!\bar\Z^+$, $S$ is a finite set, $\be\!\in\!H_2(X;\Z)$, and $J$ is an $\om$-tame almost complex structure on $X$, let $$\M_{g,S}^*(X,\be;J)\subset\ov\M_{g,S}(X,\be;J)$$ denote the subspace consisting of maps, i.e. $J$-holomorphic maps $u\!:\Si_u\!\lra\!X$ such that $\Si_u$ is a smooth (connected) Riemann surface and $u^{-1}(u(z))\!=\!\{z\}$ and $d_zu\!\neq\!0$ for some $z\!\in\!\Si_u$. These conditions imply that $u$ does not factor through a $d$-fold cover $\Si_u\!\lra\!\Si$, with $d\!>\!1$; see [@McS Section 2.5]. If $f_j\!: M_j\!\lra\!X$, $j\!\in\!S$, are smooth maps from compact oriented manifolds of even dimensions, let $$\M_{g,\f}^*(X,\be;J)= \ov\M_{g,\f}(X,\be;J)\cap
\bigg(\M_{g,S}^*(X,\be;J)\times \prod_{j\in S}M_j\bigg),$$ with $\ov\M_{g,\f}(X,\be;J)$ defined by \_ref[Mfdfn\_e]{}. If $\M_{g,\f}^*(X,\be;J)$ is a finite set consisting of regular pairs $([u],(w_j)_{j\in S})$, we will denote its signed cardinality by $E_{g,\be}^X(J,\f)$.\
If the (real) dimension of $X$ is $6$, the expected dimension of the moduli space $\ov\M_{g,S}(X,\be;J)$ is independent of the genus $g$; see \_ref[virdim\_e]{}. Thus, one can mix curve counts of different genera passing through the same constraints. Furthermore, if $\be\!\in\!H_2(X;\Z)$ and 