We consider the problem of finding a strip separating between two polygons, whose intersection with a third (convex) polygon is of maximum area. We present an optimal linear-time algorithm for computing the optimum strip. When the third polygon is not convex, the running time of the algorithm is quadratic in the size of the input. The application in mind is the piecewise-linear surface interpolation in simple branching cases, where the sought volume branches from one contour in one slice into two contours in the other slice.