The interpretation and analysis of intrapartum fetal heart rate (FHR), enabling early detection of fetal acidosis, remains a challenging signal processing task. The ability of entropy rate measures, amongst other tools, to characterize temporal dynamics of FHR variability and to discriminate non-healthy fetuses has already been massively investigated. The present contribution aims first at illustrating that a k-nearest neighbor procedure yields estimates for entropy rates that are robust and well-suited to FHR variability (compared to the more commonly used correlation-integral algorithm). Second, it investigates how entropy rates measured on multiresolution wavelet and approximation coefficients permit to improve classification performance. To that end, a supervised learning procedure is used, that selects the time scales at which entropy rates contribute to discrimination. Significant conclusions are obtained from a high quality scalp electrode database of nearly two thousands subjects collected in a French public university hospital.