In recent years, several advantages of noise radars have positioned this technology as a promising alternative to conventional radar technology. Immunity to jamming, low mutual interference, and low probability of interception are good examples of these advantages. However, the nature of random sequences introduces several issues, such as fluctuations in the range sidelobes of the autocorrelation function causing high sidelobe levels, hence not exploitable by radar systems. This study introduces the use of multi-objective evolutionary (MOE) algorithms to design noise radar waveforms with good autocorrelation properties as well as a low peak-to-average power ratio (PAPR). A set of Pareto-optimal waveforms are produced and, most importantly, entropy is introduced as a constraint in order to maintain the transmitted signal close to a full non-deterministic waveform. Moreover, a relation between PAPR and negentropy (negative entropy) is established theoretically and validated with other authors’ simulations.