We present data from an artificial language domain that suggest new contributions to the theory of syntactic triggers. Whether a learning algorithm is capable of matching the achievements of child learners depends in part on how much parametric ambiguity there is in the input. For practical reasons this cannot be established for the domain of all natural languages. Our tactic is to estimate the incidence of unambiguous triggers by examining a constructed domain of languages whose syntactic parameters and structural properties are precisely specified. We succeeded in identifying unambiguous triggers for all non-default parameter values in all languages in this domain. In order to do so, we had to invoke between-parameter relations which disambiguate triggers that otherwise would have been parametrically ambiguous. The discovery of unambiguous triggers in this artificial domain does not prove a sufficiency in natural languages, but it may revive investigation of the psychological plausibility of deterministic models of human language acquisition. (Contains 3 figures, 5 tables, and 55 footnotes.)