With the growing scaling of technology, leakage power dissipation has become a critical issue of VLSI circuits and systems designs. Multi-threshold CMOS leads to about 10X leakage reduction in circuit standby mode. In this paper, we reduce leakage current through fine-grain sleep transistor (ST) insertion which makes it easier to guarantee circuit functionality at high speed and improves circuit noise margins [1]. We model the leakage current reduction problem as a mixed-integer linear programming (MLP) problem in order to simultaneously choose where to add the sleep transistors and the sleep transistors? sizes optimally. The model is solved with both continuous (MLP-C) and discrete (MLP-D) sleep transistor size constraints. Furthermore a method to speed up MLP-D model is introduced. Because of the better circuit slack utilization, our experimental results show that the MLP-C model can achieve 79.75%, 93.56%, 94.99% leakage saving when the circuit slow down is 0%, 3%, 5% respectively. The MLP-C model also achieves on average 74.79% less area penalty compared to the conventional fixed slowdown method when the circuit slowdown is 7%. The MLP-D model can achieve similar leakage saving compared to the MLP-C model. The MLP-CtoD method can speed up the MLP-D model 30X times with almost no difference in leakage reduction.