The use of commercial-off-the-shelf (COTS) products creates a software integration problem, whether a single COTS software component is being integrated into a software system, or the whole system is being built primarily from COTS products. This integration may require considerable effort and affect system quality. A good estimate of integration cost can help in the decision of whether or not to use a COTS solution, the selection of the best COTS products, and determine the amount and type of glueware that needs to be built. In this paper, we introduce a set of variables that have the potential to estimate the integration cost. We present a classification scheme of software architectures with respect to the integration of COTS products. The scheme is based on inter-component interactions within software architectures. The classification scheme allows the comparison of integration costs of different COTS products relative to different software architectures.