One of the remaining challenges for the scientific-technical community is predicting preterm births, for which electrohysterography (EHG) has emerged as a highly sensitive prediction technique. Sample and fuzzy entropy have been used to characterize EHG signals, although they require optimizing many internal parameters. Both bubble entropy, which only requires one internal parameter, and dispersion entropy, which can detect any changes in frequency and amplitude, have been proposed to characterize biomedical signals. In this work, we attempted to determine the clinical value of these entropy measures for predicting preterm birth by analyzing their discriminatory capacity as an individual feature and their complementarity to other EHG characteristics by developing six prediction models using obstetrical data, linear and non-linear EHG features, and linear discriminant analysis using a genetic algorithm to select the features. Both dispersion and bubble entropy better discriminated between the preterm and term groups than sample, spectral, and fuzzy entropy. Entropy metrics provided complementary information to linear features, and indeed, the improvement in model performance by including other non-linear features was negligible. The best model performance obtained an F1-score of 90.1 ± 2% for testing the dataset. This model can easily be adapted to real-time applications, thereby contributing to the transferability of the EHG technique to clinical practice.