N-jettiness subtractions provide a general approach for performing fully-differential next-to-next-toleading order (NNLO) calculations. Since they are based on the physical resolution variable N-jettiness, T N , subleading power corrections in τ ¼ T N =Q, with Q a hard interaction scale, can also be systematically computed. We study the structure of power corrections for 0-jettiness, T 0 , for the gg → H process. Using the soft-collinear effective theory we analytically compute the leading power corrections α s τ ln τ and α 2 s τln 3 τ (finding partial agreement with a previous result in the literature), and perform a detailed numerical study of the power corrections in the gg, gq, and qq channels. This includes a numerical extraction of the α s τ and α 2 s τ ln 2 τ corrections, and a study of the dependence on the T 0 definition. Including such power suppressed logarithms significantly reduces the size of missing power corrections, and hence improves the numerical efficiency of the subtraction method. Having a more detailed understanding of the power corrections for both qq and gg initiated processes also provides insight into their universality, and hence their behavior in more complicated processes where they have not yet been analytically calculated.