The paper presents a construction of subfield subcodes from generalized Reed-Solomon codes that is similar to classical Goppa codes, but simpler. Following an idea of Roseiro et al, we use Delsarte's theorem to create subfield subcodes of larger than expected dimension by ensuring their duals, which are trace codes, have small dimension. This method produced several codes over ${\mathbb F}_5$, ${\mathbb F}_3$ and ${\mathbb F}_2$ that beat the best known codes, and numerous others that match the best know parameters.