Principle A of the Binding Theory states that an anaphor must be A-bound in the local domain containing it, its governor and an accessible subject. However, if the anaphor is contained in an infinitival complement clause, it may, in North Sami, be bound either by the clause-mate subject or by the subject of the tensed clause. Thus, it appears that there is a larger binding domain for anaphors in addition to that determined by the condition A of standard binding theory. This domain can in some languages, as in North Sami, be defined by the notion of Tense whereas in other languages this need not be case, as in English. This supports the approach that the characterization of binding domains is parameterized and that languages pick different values of the parameter.