Formally describing and analysing quantitative requirements of software components might be important in software engineering; in the paradigm of API-based software systems might be vital. Quantitative requirements can be thought as characterising the Quality of Service – QoS provided by a service thus, useful as a way of classifying and ranking them according to specific needs. An efficient and automatic analysis of this type of requirements could provide the means for enabling dynamic establishing of Service Level Agreements – SLA, allowing for the automatisation of the Service Broker.In this paper we propose the use of a language for describing QoS contracts based on convex specification, and a two-phase analysis procedure for evaluating contract satisfaction based on the state of the art techniques used for hybrid system verification. The first phase of the procedure responds to the observation that when services are registered in repositories, their contracts are stored for subsequent use in negotiating SLAs. In such a context, a process phase of contract minimisation might lead to great efficiency gain when the second, and recurrent, phase of determining QoS compliance is run.