Transcription factors and the short, often degenerate DNA sequences they recognize are central regulators of gene expression, but their regulatory code is challenging to dissect experimentally. Thus, computational approaches have long been used to identify putative regulatory elements from the patterns in promoter sequences. Here we present a new algorithm "POWRS" (POsition-sensitive WoRd Set) for identifying regulatory sequence motifs, specifically developed to address two common shortcomings of existing algorithms. First, POWRS uses the position-specific enrichment of regulatory elements near transcription start sites to significantly increase sensitivity, while providing new information about the preferred localization of those elements. Second, POWRS forgoes position weight matrices for a discrete motif representation that appears more resistant to over-generalization. We apply this algorithm to discover sequences related to constitutive, high-level gene expression in the model plant Arabidopsis thaliana, and then experimentally validate the importance of those elements by systematically mutating two endogenous promoters and measuring the effect on gene expression levels. This provides a foundation for future efforts to rationally engineer gene expression in plants, a problem of great importance in developing biotech crop varieties.BSD-licensed Python code at http://grassrootsbio.com/papers/powrs/.