This study investigates children's interpretation of sentences with two logical operators: Dutch universal modal "hoeven" and negation ("niet"). In adult Dutch, "hoeven" is an NPI that necessarily scopes under negation, giving rise to a NOT > NECESSARY reading. The findings from a hidden-object task with 5- and 6-year-old children showed that children's performance is suggestive of an interpretation of sentences with "hoeft niet" in which the modal scopes over negation (NECESSARY > NOT). This is in line with the Semantic Subset Principle that dictates that children should opt for the strongest possible reading in case of potential scope ambiguities. The full pattern of results, however, seems to be determined, in addition, by a particular strategy children use when facing uncertainty called Premature Closure.