Abstract Donkey anaphora in quantified sentences is ambiguous between an existential and a universal reading. The extent to which different readings are accessible depends on the quantifier, but how to model this dependence is debated (Kanazawa, 1994; Champollion et al. 2019). This study advances this debate by providing novel experimental data on the interpretation of donkey anaphora in sentences with non-monotonic quantifiers exactly 3 and all but one. We establish that while the existential reading of donkey anaphora is the preferred one with both exactly 3 and all but one, the universal reading is accessed more with all but one than with exactly 3. These results have important implications for both Kanazawa (1994) and Champollion et al. (2019) theories, as both need to be amended to fully capture the empirical picture.