An aggregation service (AgS) is a P2P overlay-tier whose purpose is to aggregate and optimize the searching of services and service components maintained by service providers in a P2P Service Overlay Network (SON). AgS dimensioning takes into account the AgS size, in order to allow it to adequately perform the searching when compared with P2P SON native searching mechanisms. Suitable AgS dimensioning helps service providers to plan their infrastructures and services, allowing them to keep costs under control. This paper presents an assessment of the dimensioning of an AgS overlay. The assessment takes into account the searching response time as metric in both the environments: 1) P2P SON and 2) AgS. The assessment also takes into account the AgS own maintenance overhead, in order to compare it with the searching response time in the P2P SON. The simulation results show that, on average, AgSs whose sizes are lesser than 90% of the P2P SON size present better searching efficiency than the same searching operations in P2P SON.