Consider the nth integrator (x) over dot = J(n)x + sigma(u)e(n), where x is an element of R-n, u is an element of R, J(n) is the nth Jordan block and e(n) = (0 ... 0 1)(T). R-n. We provide easily implementable state feedback laws u = k(x) which not only render the closed-loop system globally asymptotically stable but also are finite-gain Lp-stabilizing with arbitrarily small gain, as in [A. Saberi, P. Hou, and A. Stoorvogel, IEEE Trans. Automat. Control, 45 (2000), pp. 1042-1052]. These L-p-stabilizing state feedbacks are built from homogeneous feedbacks appearing in finite-time stabilization of linear systems. We also provide additional L-infinity-stabilization results for the case of both internal and external disturbances of the nth integrator, namely, for the perturbed system (x) over dot = J(n)x + e(n)sigma(k(x) + d) + D, where d is an element of R and D is an element of R-n.