  While effective resolution of Thue equations has been well understood since
the work of Baker in the 1960s, similar results for norm-form equations in more
than two variables have proven difficult to achieve. In 1983, Vojta was able to
address the case of three variables over totally complex and Galois number
fields. In this paper, we extend his results to effectively resolve several new
classes of norm-form equations. In particular, we completely and effectively
settle the question of norm-form equations over totally complex Galois sextic
fields.
