This paper compares and evaluates two different control strategies for machine translation. One of them is the structure-based approach, which processes texts by means of the recursive application of rule to representations. The other is the constraint-based approach, which makes use of constraints on translational equivalence, with no commitment to sequential recursive processing. The latter, which was first developed in LFG, has a number of advantages, both conceptual and computational, but it does not fare well with a number of difficult cases for MT, such as modifier incorporation and head switching. The author shows how these cases can be dealt with by proposing some changes to the original LFG formalism.