Consumers of mobile telephone services are faced with the task of choosing from among different service providers and services. This choice making is complex and it involves making some tradeoffs among the attributes of the various services before arriving at the services most desirable to them. This study analyzed the process by which Lagos state subscribers of mobile telephone services select their desired services among some available telephone services in the market to meet their personal or corporate needs. Conjoint analysis was applied for analyzing the process which involved a trade-offs of several conflicting attributes of these telephone services by the subscribers before arriving at their choices. The respondents divided into two groups which are the private/personal calling plan (PPP) and the business/commercial calling plan (BCP). For each of the two calling plans twelve mobile telephone services attributes each with different levels were involved. The results show that for both calling plans, the subscribers have preference for MTN, followed by Zain and then Glo among the calling plan providers. They also show preference for the following service attributes, unlimited anytime minutes, unlimited free night calls, free weekend calls, international geographical coverage, complete control over credit usage and per second billings. Geographical coverage, control over credit usage and weekend minutes were three most important service attributes to them.