Differentiated services (DiffServ) and multiprotocol label switching (MPLS) are attracting attention as quality of service (QoS) technologies for the large-scale Internet. DiffServ cannot offer end-to-end QoS by itself, because it controls per-hop packet forwarding order with relative priority according to its class. Achieving end-to-end QoS requires traffic engineering support by using MPLS and constraint-based routing (CBR) schemes in addition to DiffServ. CBR schemes compute explicit routes for label-switched paths (LSPs), which specify packet forwarding routes in MPLS networks. We assume two DiffServ classes: expedited forwarding (EF) class, which corresponds to voice traffic requiring a low path delay, and best effort (BE) class which corresponds to data traffic requiring high throughput. Five DiffServ-aware CBR schemes are constructed, based on route computation algorithms and LSP-types depending on whether or not DiffServ classes are considered. By simulating a path arrangement for two class traffic between every node pair, we evaluate the QoS achieved by the five DiffServ-aware CBR schemes. The results show that the scheme that uses a different route computation algorithm for each DiffServ class can offer better QoS for each class.