In this work, new plain and composite high-energy solitons of the cubic–quintic Swift–Hohenberg equation were numerically found. Starting from a composite pulse found by Soto-Crespo and Akhmediev and changing some parameter values allowed us to find these high energy pulses. We also found the region in the parameter space in which these solutions exist. Some pulse characteristics, namely, temporal and spectral profiles and chirp, are presented. The study of the pulse energy shows its independence of the dispersion parameter but its dependence on the nonlinear gain. An extreme amplitude pulse has also been found.