The literature provides several structural decomposition methods for identifying tractable subclasses of the constraint satisfaction problem. Generalized hypertree decomposition is the most general of such decomposition methods. Although the relationship to other structural decomposition methods has been thoroughly investigated, only little research has been done on efficient algorithms for computing generalized hypertree decompositions. In this paper we propose new heuristic algorithms for the construction of generalized hypertree decompositions. We evaluate and compare our approaches experimentally on both industrial and academic benchmark instances. Our experiments show that our algorithms improve previous heuristic approaches for this problem significantly.