This paper focuses on parallel query optimization. We consider the operator problem and introduce a new class of execution strategies called Linear-Oriented Bushy Trees (LBTs). Compared to the related approach of Bushy Trees (BTs) a significant complexity reduction of the operator ordering problem, while not loosing quality, can be derived theoretically and demonstrated later on experimentally. In addition, we applied LBTs to parallel query optimizers using an enumerative search technique, like the parallel query optimizer of Microsoft SQL Server [1]. To do this, we propose necessary modifications to the exploring strategy of the search technique. An effective memoizing structure is reused and its size for the space of LBTs is computed. In order to guarantee the efficiency of the optimization process, a duplicate-free transformation rule set for the generation of LBTs is introduced and its correctness is proven. Finally, we summarize selected performance results to give a flavor of th...