This paper reports on how adult Japanese Learners of English/JLEs acquire universal and parameterised constraints which regulate the accessibility of Goals to Wh-Movement, and which determine whether subordinate or superordinate material is pied-piped or stranded when a whword is moved. We present evidence that universal constraints on Goal Accessibility operate in early JLE grammars, and that learners initially transfer setting for parameterised constraints from L1 to L2, concluding that our overall findings are broadly consistent with the Full Transfer Full Access model of L2 acquisition developed in Schwarz and Sprouse (1994, 1996). We show that JLEs are able to reset some parameterised constraints (e.g. the P-Stranding Constraint) but not others (e.g. the Left Branch Condition), and argue that they are only able to re-set learnable parameterised constraints (i.e. those whose setting can be learned solely on the basis of positive evidence from input), not unlearnable parameterised constraints (i.e. those whose settings cannot be learned solely on the basis of positive input).