The Internet of Things (IoT) refers to the interconnection of billions of constrained devices, denoted as “smart objects” (SO), in an Internet-like structure. SOs typically feature limited capabilities in terms of computation and memory and operate in constrained environments, such low-power lossy networks. As IP has been foreseen as the standard for smart-object communication, an effort to bring IP connectivity to SOs and define suitable communication protocols (i.e. CoAP) is being carried out within standardization organisms, such as IETF. In this paper, we propose a constrained version of the Session Initiation Protocol (SIP), named “CoSIP”, whose intent is to allow constrained devices to instantiate communication sessions in a lightweight and standard fashion. Session instantiation can include a negotiation phase of some parameters which will be used for all subsequent communication. CoSIP can be adopted in several application scenarios, such as service discovery and publish/subscribe applications, which are detailed. An evaluation of the proposed protocol is also presented, based on a Java implementation of CoSIP, to show the benefits that its adoption can bring about, in terms of compression rate with the existing SIP protocol and message overhead compared with the use of CoAP.