Constraint programming has been proved as an excellent tool to solve combinatorial problems in many application areas. Through constraint propagation large parts of the search space can be pruned away. Hard problems are those which involve disjunctive constraints introducing non-determinism. While the introduction of choice-points for disjunctive constraints may lead to combinatorial explosion, other approaches only check whether the disjunction can still be satisfied. Constructive disjunction instead lifts common information of alternatives up and thus allows other parts of the computation to benefit from this extra information. This form of propagation improves pruning of search spaces for certain classes of problems, such as scheduling, time tabling and the like, enormously. We present how to realize constructive disjunction for finite domain constraints without local computation spaces in the concurrent constraint language Oz. The implementation is achieved with minimal effort reusing existing concepts. Our implementation scheme is suited for other constraint systems based on arc-consistency algorithms too.