This chapter considers various heuristics which can be used by spellers who feel uncertain about the spelling of particular English biconstituent compounds. Based on the statistically significant variables from the empirical study, several types of algorithm were tested (e.g. a comprehensive algorithm and a take-the-best algorithm). The CompSpell algorithm (which uses merely the three features part of speech of the compound, length of the compound measured in syllables and length of the second constituent measured in letters) emerges as a maximally efficient algorithm aiming for a compromise between comparatively large prediction accuracy and a comparatively small number of features. Its predictive accuracy ranges between 61.0% and 80.7% for different types of compound list, with results that are highly similar to those of two educated native speakers of British English. Since the CompSpell algorithm can be expected to predict the spelling of roughly three out of four compounds for all parts of speech correctly, its simplicity and efficiency make it a desirable complementation of existing material in the teaching of English as a foreign language. More advanced learners (but also native speakers of English) may use the algorithm as a decision instrument in cases where their intuition can provide no guidance.