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High peak-to-average power ratio (PAPR) is a critical problem in orthogonal frequency-division multiplexing (OFDM). The fifth-generation New Radio (5G NR) facilitates the utilization of multiple heterogeneous bandwidth parts (BWPs), which complicates the PAPR problem even further and introduces inter-numerology interference (INI) between the BWPs. This letter proposes two novel schemes to reduce the PAPR of mixed-numerology OFDM signals. The first scheme is an original enhanced iterative clipping-and-error-filtering (ICEF) approach that cancels efficiently the INI along with PAPR reduction. This allows to achieve efficient PAPR reduction while being compatible with well-known windowed overlap-and-add (WOLA) processing. The second scheme is based on fast-convolution (FC) processing, where PAPR reduction is embedded in the FC filtering carried out using overlapping processing blocks. This allows one to use any existing block-wise PAPR reduction method to reduce the composite signals' PAPR with arbitrary BWP waveforms, and it is thus especially well suited for processing mixed-numerology composite waveforms carrying multiple BWPs with different OFDM numerologies. The performance of the proposed algorithms is evaluated in the 5G NR context, and the essential performance advantages are demonstrated and quantified.