Previous work on automated error recognition and correction of texts written by learners of English as a Second Language has demonstrated experimentally that training classifiers on error-annotated ESL text generally outperforms training on native text alone and that adaptation of error correction models to the native language (L1) of the writer improves performance. Nevertheless, most extant models have poor precision, particularly when attempting error correction, and this limits their usefulness in practical applications requiring feedback. We experiment with various feature types, varying quantities of error-corrected data, and generic versus L1-specific adaptation to typical errors using Naïve Bayes (NB) classifiers and develop one model which maximizes precision. We report and discuss the results for 8 models, 5 trained on the HOO data and 3 (partly) on the full error-coded Cambridge Learner Corpus, from which the HOO data is drawn.