The rough idea of Woodward et al. is to introduce interior marked points, constrained to lie on a Donaldson divisor $D$ disjoint from the Lagrangians. The virtual dimension is not affected by these divisor constraints, since each interior marked point increases it by 2, while each divisor constraint decreases it by 2. One needs to arrange $D$ to be of sufficiently high degree, so that each nontrivial pseudoholomorphic disk with boundary on the Lagrangians has at least one intersection with $D$. On a teardrop curve, imposing the divisor constraint at interior marked points kills the domain automorphisms $Aut(D^{2},1)$, so one can then introduce domain dependent perturbation of almost complex structures compatible with $D$ to achieve sufficient transversality to make sense of counts. The appealing feature of this approach, is that adding marked points does not alter the geometric interpretation of the holomorphic curves, so stays closer to geometry than the virtual approach.

The framework of Woodward et al. [81][82] is not restricted to exact settings, and works also for compact symplectic manifolds with rational $[\omega]\in H^{2}(X)$. Producing the Donaldson divisor with the intersection properties is easier if $[\omega]\in H_{2}(X,L)$ is a rational class, although the methods in [14, section 3.1] allows one to largely relax this assumption.

In exact manifolds, as mentioned in [81, Remark 4.5], one can avoid the spherical components of the treed disks. In the exact Lagrangian setting, the only bubbling happens at the self intersection points. These afford significant simplifications to the construction, and allows one to think of the treed disks in [14][15] [81][82] in terms of a tree of holomorphic polygons connected at the self intersection points. By avoiding the troublesome sphere bubbles, one can also relax the restriction of moduli spaces of dimension at most one.