Cognates share their form and meaning across languages: “winter” in English means the same as “winter” in Dutch. Research has shown that bilinguals process cognates more quickly than words that exist in one language only (e.g. “ant” in English). This finding is taken as strong evidence for the claim that bilinguals have one integrated lexicon and that lexical access is language non-selective. Two English lexical decision experiments with Dutch–English bilinguals investigated whether the cognate facilitation effect is influenced by stimulus list composition. In Experiment 1, the ‘standard’ version, which included only cognates, English control words and regular non-words, showed significant cognate facilitation (31 ms). In contrast, the ‘mixed’ version, which also included interlingual homographs, pseudohomophones (instead of regular non-words) and Dutch-only words, showed a significantly different profile: a non-significant disadvantage for the cognates (8 ms). Experiment 2 examined the specific impact of these three additional stimuli types and found that only the inclusion of Dutch words significantly reduced the cognate facilitation effect. Additional exploratory analyses revealed that, when the preceding trial was a Dutch word, cognates were recognised up to 50 ms more slowly than English controls. We suggest that when participants must respond ‘no’ to non-target language words, competition arises between the ‘yes’- and ‘no’-responses associated with the two interpretations of a cognate, which (partially) cancels out the facilitation that is a result of the cognate's shared form and meaning. We conclude that the cognate facilitation effect is a real effect that originates in the lexicon, but that cognates can be subject to competition effects outside the lexicon.