Combined-optimal designs (Li and Lin, 2003) are obviously the best choices for the initial designs if we partition the experiment into two parts with equal size to obtain some information about the process, especially for the case not considerign the blocking factor. In this pape, the definition of combined-optimal design is extended to the case when blocking factor is significant, and this new class of designs is called blocded combined-optimal designs. Some general results are obtained which relate 2k-pIII inital designs with their complementary designs when k>5n8, where n=2k-p. By applying these results, we are able to characterize 2k-pIII combined-optimal designs or blocked combined-optimal dwdigns in terms of their complementary designs. It is also proved that both 2k-pIII compbined-optimal and blocked combined-optimal designs are not minimum aberration designs when k>5n8 and n-1-k>2. And some combined-optimal and bloked combined -optimal designs with 16 and 32 runs are constructed fo rillustration.