Parallelism constraints are logical desciptions of trees. They are as expressive as context unification, i.e. second-order linear unification. We present a semi-decision procedure enumerating all most general unifiers of a parallelism constraint and prove it sound and complete. In contrast to all known procedures for context unification, the presented procedure terminates for the important fragment of dominance constraints and performs reasonably well in a recent application to underspecified natural language semantics.