This paper investigates the issue of “predistorter blow-up,” i.e., uncontrolled peak expansion caused by the predistorter. To control the peak expansion, an extension of the multistep indirect learning architecture (MS-ILA) is proposed by adding a constraint that describes the allowed peak power of the predistortion signal. The resulting optimization problem is shown to be convex and an optimization method is formulated to solve it. Measurements on a class-AB power amplifier (PA) using orthogonal frequency-division multiplex signals show that the peak control works as intended and prevents the MS-ILA from generating high peaks when the PA is operated in compression. The restriction on the peak power also prevents the performance degradation occurring due to the “blow-up” problem. This makes the proposed controlled MS-ILA a safer option than the standard MS-ILA. In addition to controlling the peak input power to the PA, using the proposed method it was possible to increase the output power by 1.3 dB while fulfilling requirements of less than 40-dB adjacent channel leakage power ratio, compared to the standard five-step MS-ILA. Reduced peak power also reduces the requirements on linearity in signal generation, resolution in computations, and analog-to-digital and digital-to-analog conversion.