The sensitivity of a family of high-gain inertial confinement fusion (ICF) targets to implosion nonuniformities is studied by means of 2-D numerical simulations. The effect of single-wavelength, low-mode number perturbations of the driving pressure is considered. It is shown that the ratio Q of the 2-D target yield to the yield obtained in the spherically symmetric case is a function of the perturbation parameters as well as of the spark convergence ratio and of the 1-D ignition margin of the target. The scaling of Q with mode number and amplitude is derived; it is also shown that tolerable levels of nonuniformities depend critically on the 1-D ignition margin.