The $N$-jettiness slicing method has become a standard tool for precision QCD calculations over the past decade. However, achieving reliable numerical stability requires the inclusion of power corrections beyond leading power in the slicing variable. We present the computation of the next-to-leading power (NLP) corrections for both zero-jettiness and one-jettiness at next-to-leading order (NLO). We outline the methodology to systematically compute these NLP corrections and investigate whether the process independence observed at leading power extends to NLP for color-singlet final states. For the zero-jettiness case, we derive a master formula that captures both soft and collinear subleading contributions in a unified framework, allowing for efficient evaluation of power corrections in high-multiplicity processes. We also present the first explicit NLP calculation for one-jettiness process at NLO, focusing on prompt-photon production using a realistic jet algorithm. These results give key insights into the subleading contributions to the cross sections for slicing variables and the applicability of $N$-jettiness slicing in collider phenomenology.