ingredients controlling superconductivity in the array of 4-leg Hubbard ladders that we have considered in this letter, are a small residual Fermi surface (either pockets as in Scenario I or arcs as in Scenario II), which is coupled in the d-wave Cooper channel to a finite energy Cooperon associated with the pseudogap responsible for the partial truncation of the Fermi surface. The properties of a weak coupling 4-leg Hubbard ladder near to half-filling are used to obtain these key ingredients. Our goal is to derive a tractable model containing the important features that are relevant to high temperature superconductivity in the cuprates. In order to assess the relevance of our model to this goal, clearly one must examine whether these key ingredients are present in a two dimensional Hubbard model on a square lattice near half-filling. As we mentioned above, earlier numerical renormalization group studies on the 2- dimensional Hubbard model were interpreted as pointing towards a similar pairing mecha- nism arising from enhanced pairing correlations present in a condensate that truncates the Fermi surface in the antinodal regions. There are of course two reservations in these earlier works. Firstly, the one loop approximation in the numerical renormalization group stud- ies limits them to at most moderately strong onsite repulsive interactions. Secondly, the renormalization group studies per se break down when the scattering vertices flow to strong coupling and the nature of the resulting low energy or low temperature effective action is a difficult problem which could only be surmised rather than explicitly derived. These two weaknesses make it imperative to examine the question whether these key ingredients are present also for strong coupling. The most reliable strong coupling calculations are exact diagonalization studies of strong coupling Hamiltonians. The only limitation is the finite cluster size which currently is limited to small clusters containing up to 32 sites and 1,2 and 4 holes. Leung and his collaborators Refs. 37–39 have reported a series of calculations for these clusters using the strong coupling t-J model and its extensions to include longer range hopping and interactions. We begin with a recap of the main conclusions of these calculations. The allowed set of k -points in a 32-site cluster with periodic boundary conditions contain both the four nodal ( π/ 2 , π/ 2) and two antinodal points ( π, 0) and (0 , π ). A single hole enters at a nodal point. For two holes there are two different states that are possible groundstates depending on the parameter values. For the plain t-J model with only nearest neighbour hopping a 2-hole bound pair state with d( x 2 − y $^{2}$) symmetry is the groundstate on the 32-site cluster for J/t > 0.28. The 17