In order to apply sphere decoding algorithm in multiple-input multiple-output communication systems and to make it feasible for real-time applications, its computational complexity should be decreased. To achieve this goal, this paper provides some useful insights into the effect of initial and the final sphere radii and estimating them effortlessly. It also discusses practical ways of initiating the algorithm properly and terminating it before the normal end of the process as well as the cost of these methods. Besides, a novel algorithm is introduced which utilizes the presented techniques according to a threshold factor which is defined in terms of the number of transmit antennas and the noise variance. Simulation results show that the proposed algorithm offers a desirable performance and reasonable complexity satisfying practical constraints.