Supporting IPv6/UDP/CoAP protocols over Low Power Wide Area Networks (LPWANs) can bring open networking, interconnection, and cooperation to this new type of Internet of Things networks. However, accommodating these protocols over these very low bandwidth networks requires efficient header compression schemes to meet the limited frame size of these networks, where only one or two octets are available to transmit all headers. Recently, the Internet Engineering Task Force (IETF) LPWAN working group drafted the Static Context Header Compression (SCHC), a new header compression scheme for LPWANs, which can provide a good compression factor without complex synchronization. In this paper, we present an implementation and evaluation of SCHC. We compare SCHC with IPHC, which also targets constrained networks. Additionally, we propose an enhancement of SCHC, Layered SCHC (LSCHC). LSCHC is a layered context that reduces memory consumption and processing complexity, and adds flexibility when compressing packets. Finally, we perform calculations to show the impact of SCHC/LSCHC on an example LPWAN technology, e.g. LoRaWAN, from the point of view of transmission time and reliability.