The non-Gaussian random shaker testing with kurtosis control has been known as a way of increasing the excitation crest factor in order to realistically simulate ground vehicle vibrations and other situations when the time history includes extreme peaks higher than those appearing in Gaussian random signals. However, an opposite action is also useful in other applications, particularly in modal testing. If the PSD is the only test specification, more power can be extracted from the same shaker if the crest factor is decreased and an extra space is created between the peaks of reduced height and the system abort limit. To achieve this, a technique of sigma clipping is commonly used but it generates harmonic distortions reducing dynamic range of shaker system. It is shown in the paper that the non-Gaussian phase selection in the IFFT generation can reduce kurtosis to 1.7 and bring the crest factor of drive signals from 4.5 to 2. The phase selection method does this without any loss of the controller's dynamic range that inevitably occurs after sigma clipping or polynomial transformation of time histories.