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Advances in optical equipment permit network carriers to offer lightpath-on-demand services to Internet service providers (ISPs). These services are the key for constructing cost-efficient virtual topology capacity adjustment (VTCA) schemes, where ISPs dynamically adapt the number of lightpaths contracted between their IP routers, according to time-varying traffic volumes. An existing technique called lightpath bundling offers ISPs the possibility of grouping lightpaths between the same pair of routers into so-called bundles, perceived by the IP layer as single virtual links of aggregated capacity. Consequently, new lightpaths added or removed from bundles are not seen by the IP layer as new links necessary to advertise, but simply as capacity adjustments of already existing links. Adding lightpath bundling to the picture opens the door for developing VTCA schemes which maintain stability in the IP routing tables, a major requirement for ISPs. In this paper, we present and evaluate the merits of the proposed stable routing VTCA (SR-VTCA) paradigm and present algorithms for designing such a scheme. The results clearly show that SR-VTCA gives an advantageous trade-off between the fully static network with no capacity adjustment and the fully dynamic VTCA scheme where both the IP routing and the VT are reconfigured over time.