In this patper, some relationships between offsets and total delay were obtained from simple traffic simulation on small-scale signalized streets under the over-saturated conditions, from which some considerations were given about optimal offsets. Green times of each signal and common cycle length are given and only relative offsets are variables. Total delay is made up of delay at each link on main street. Findings are as follows : If only one direction is congested, preferential offset for uncongested direction is optimal. If both directions are congested, it is optimal to give preferential offset to each link of either direction. If traffic demands from cross streets through turning movements enter the main street and make it congested, it is difficult to optimize the offset from a viewpoin of total delay on main street. In addition, it was shown that such offsets that can maintain saturation flow during the green time at downstream signal are essential if the link is short and the storage capacity is lower than throughput capacity at the signal.