The augmented block design is widely used in breeding programs. Control(s) used to estimate the experimental error. Generally augmented designs use large number of blocks and unreplicated designs. In this design, we cannot measure the error mean square. Therefore, augmented block designs are less efficient. The main objective of this study was constructing efficient designs by using BIB design, modified augmented designs. The study establishes a marriage between test versus control treatment through in both RIB design, augmented block design, and balanced main effect plans (saturated and unsaturated)with BIB designs, modified augmented designs. The construction and the analysis of modified augmented BIB design can be considered by using the fixed and mixed model analysis, and in addition, the A- and MV- Optimality of those designs have been provided with illustrative examples. The results were obtained using SAS. Based on our finding, the modified augmented design is more efficient than augmented designs.