Standard lift-and-project cuts are derived from a disjunction by solving a cut generating linear program (CGLP) to optimize the multipliers associated with the inequalities on the two sides of the disjunction. These cuts are then strengthened by optimally modularizing the cut coefficients of the integer-constrained variables. Clearly, the result is not an overall optimum. Simultaneous optimization under both aspects is a hard nonlinear integer programming problem. We approximate this overall optimum in the context of generating lift-and-project cuts from the LP simplex tableau by applying disjunctive modularization to the source row for the cut after each pivot. Computational experience will be presented.