The dative alternation poses a learnability paradox: when children hear give money to him and give him money, they could formulate a rule deriving the double object from the prepositional form, but the rule would allow overgeneralization from donate money to him to donate him money. Children are not corrected for speaking ungrammatically, so how do they avoid overgeneralizing? The ‘conservatism’ hypothesis proposes that children do not generalize at all; the ‘criteria’ hypothesis holds that children learn to constrain their rule to apply to monosyllabic verbs denoting possession changes. In a questionnaire study, adults rated double-object forms with novel verbs as sounding better if they met these criteria. In an analysis of speech transcripts, children were found to produce ungrammatical double-object sentences (though not very frequently). In two experiments children were taught novel motion verbs; they extended them to double-object structures, and did so more often for monosyllabic than for polysyllabic verbs and more often to denote a possession transfer than motion to a location. However, children also had a bias to use each verb in the construction they heard it in. Thus children are not invariably conservative but show conservative tendencies, and their generalizations are influenced by morphophonological and semantic criteria. We propose that speakers acquire a dative rule that operates on two levels: a broad-range rule defines the possibility of a verb meaning ‘cause to move’ to be changed into one meaning ‘cause to have’, and narrow-range rules license such extensions to be made for subclasses of semantically and morphologically similar verbs.