A 16-channel gated integrator (GI) module following semi-Gaussian shaping amplifiers was developed for high-resolution energy spectroscopy systems at Institute of Modern Physics, Chinese Academy of Sciences. This GI solved the ballistic deficit problem by integrating the signal until all the charge was collected from the detector at counting rates up to 100 K. In this paper, a fast shaper was used to optimize the gate logic to ensure nonlinearity of the GI less than 0.17%; and a novel compensation approach, to reduce the charge injection from the switches in the GI; and a T-switch configuration, to eliminate leakage current in the reset switch.