The dawn of the Internet of Things (IoT) paradigm has brought about a series of novel services never imagined until recently. However, certain deployments such as those employing Low-Power Wide-Area Network (LPWAN)-based technologies may present severe network restrictions in terms of throughput and supported packet length. This situation prompts the isolation of LPWAN systems on islands with limited interoperability with the Internet. For that reason, the IETF's working group has proposed a Static Context Header Compression (SCHC) scheme that permits compression and fragmentation of and IPv6/UDP/CoAP packets with the aim of making them suitable for transmission over the restricted links of LPWANs. Given the impact that such a solution can have in many IoT scenarios, this paper addresses its real evaluation in terms not only of latency and delivery ratio improvements, as a consequence of different compression and fragmentation levels, but also of the overhead in end node resources and useful payload sent per fragment. This has been carried out with the implementation of middleware and using a real testbed implementation of a LoRaWAN-to-IPv6 architecture together with a publish/subscribe broker for CoAP. The attained results show the advantages of SCHC, and sustain discussion regarding the impact of different SCHC and LoRaWAN configurations on the performance. It is highlighted that necessary end node resources are low as compared to the benefit of delivering long IPv6 packets over the LPWAN links. In turn, fragmentation can impose a lack of efficiency in terms of data and energy and, hence, a cross-layer solution is needed in order to obtain the best throughput of the network.