Software process improvement (SPI) initiatives are based upon an appropriate assessment of the actual state or maturity of processes and a concrete model to guide engineers in the next steps to move from the actual state to an improved one. In the context of an SPI initiative at the Chilean National Customs Service, we used the SEMAT Kernel to assess software processes and to guide the implementation of practices for their improvement. We present in this paper our experience using the SEMAT Kernel. We also present a description of several lessons learned in this experience.