As an alternative to standard response surface methodology, Cheng and Wu (2001) proposed a strategy to perform factor screening and response surface exploration on the same experiment using one design. Running a uni-stage experiment has the advantages of saving experimentation time and run size. In this article, a set of optimality criteria is proposed to assess the performance of designs for factor screening, projection, and response surface exploration, and a three-step approach is proposed for searching optimal designs. Combinatorial and algorithmic construction methods are proposed for generating new designs. Level permutation methods are used for improving the eligibility and estimation efficiency of the projected designs. The techniques are then applied to search for best three-level designs with 18 and 27 runs. Many new, more efficient and practically useful nonregular designs are found and their properties discussed.