The selection of the most acceptable architecture of e-services system is very important issue. One and the same e-service can be designed using different alternative architectures. Each system has different execution indices that are very important for the e-services clients and providers. This article shows solutions for compromise or the most acceptable selection of the architecture of e-services system using more than one criterion at the same time. The solution is based on the theory of graphs and usage of multi-criteria methods and their basics is following: E-service algorithm is described with an algorithm graph. Using segmentation of algorithm graph web service graphs are obtained that are assessed with characteristic numerical values of system architecture. Several characteristics of system architecture are: Reusability, Costs of Production and Time of Execution. The task of multi-criteria optimization of web service graphs is defined when as result the compromise or the Pareto set of web service graphs is evaluated. The most acceptable solution of system architecture is selected from Pareto set by using additional information. The usage of offered method is demonstrated with help of practical example.