Graph grammars are used for computational design synthesis (CDS) in which engineering knowledge is formalized using graphs to represent designs and rules that describe their transformation. Most engineering tasks require both topologic and parametric rules to generate designs. The research presented in this paper compares different strategies for rule application to combine topologic and parametric rules during automated design synthesis driven by a search process. The presented strategies are compared considering quantity and quality of the generated designs. The effect of the strategies, the selected search algorithm, and the initial design, from which the synthesis is started, are analyzed for two case studies: gearbox synthesis and bicycle frame synthesis. Results show that the effect of the strategy is dependent on the design task. Recommendations are given on which strategies to use for which design task.