The universal filtered multicarrier (UFMC), which has emerged as a product of the intensive studies carried out for developing alternative waveforms compatible with the oncoming fifth generation (5G) technology, has rapidly become one of the few waveforms considered seriously to be utilized in the next generation telecommunication systems due to its exclusive features. However, high peak-to-average power ratio (PAPR) problem specific to the multicarrier waveforms is waiting for researchers as the primary issue to be tackled in the UFMC waveform. To address this issue, an efficient PAPR reduction scheme called discrete cuckoo search algorithm-based selective mapping (DCS-SLM) is suggested in this paper. While creating the proposed DCS-SLM scheme, in order to make the original CS algorithm suitable to be integrated into the conventional SLM method, a novel DCS algorithm was developed. Thanks to the related DCS algorithm, it becomes possible in the SLM technique to perform phase sequence optimization, which is a combinatorial optimization process that can be carried out in discrete space. It is clearly observed from the simulation results that the integration of our novel DCS algorithm to create a new PAPR reduction technique called DCS-SLM leads to a remarkable performance improvement in the conventional SLM method due to the DCS-based phase optimization through which the PAPR of UFMC signals are reduced to minimum levels.