Constrained cost minimization in QoS routing for multipoint communication groups is the problem of path construction to achieve efficiency of group communication while meeting the delay-bound of the application. Proposed models to date, using the source- or core- based approches, search solely a subdomain of the solution space. In this paper, we analyze this problem, and propose a new solution, SPAN. Our model executes on multiple metrics for constrained multipoint communication, and spans the entire range of solutions in its search. SPAN is distributed, and generates concsistently more efficient results compared to the existing algorithms in the literature.