Non-uniform step-size distribution is implemented for split-step based nonlinear compensation in single-channel 112-Gb/s 16 quadrature amplitude modulation (QAM) transmission. Numerical simulations of the system including a 20 \times 80 km uncompensated link are performed using logarithmic step size distribution to compensate signal distortions. 50% of reduction in number of steps with respect to using constant step sizes is observed. The performance is further improved by optimizing nonlinear calculating position (NLCP) in case of using constant step sizes while NLCP optimization becomes unnecessary when using logarithmic step sizes, which reduces the computational effort due to uniformly distributed nonlinear phase for all successive steps.