In general, techniques are described for improving network path computation for requested paths that include a chain of service points that provide network services to traffic flows traversing the requested path through a network along the service chain. In some examples, a controller network device receives a request for network connectivity between a service entry point and a service exit point for a service chain for application to packet flows associated to the service chain. The device, for each pair of the service points in the particular order and using the active topology information, computes at least one end-to-end sub-path through the sub-network connecting the pair of the service points according to a constraint and computes, using the at least one end-to-end sub-path for each pair of the service points, a service path between the service entry point and the service exit point for the service chain.