In this paper, we propose a nonlinear companding technique called 'trapezoidal power companding' to reduce the high peak-to-average power ratio (PAPR) in a complex OFDM or FBMC system by transforming the original signals into new signals whose power is trapezoidally distributed. A flexible parameter is used to determine the shape of the trapezium so that the proposed scheme is able to meet the requirements for various conditions. Given an expected PAPR value, the scheme provides a closed-form solution that guarantees the actual PAPR the same as the expected. Simulation results show that the proposed scheme offers a trade-off in terms of the complementary cumulative distribution function (CCDF) of PAPR, out-of-band radiation and bit error rate (BER). A comparison with another flexible companding scheme in  shows that our proposed scheme has better BER performance and has a perfect theoretical prediction of the actual PAPR values.