In this paper we describe a new method combining the polynomial neural network and decision tree techniques in order to derive comprehensible classification rules from clinical electroencephalograms (EEGs) recorded from sleeping newborns. These EEGs are heavily corrupted by cardiac, eye movement, muscle and noise artifacts and as a consequence some EEG features are irrelevant to classification problems. Combining the polynomial network and decision tree techniques, we discover comprehensible classification rules whilst also attempting to keep their classification error down. This technique is shown to outperform a number of commonly used machine learning technique applied to automatically recognize artifacts in the sleep EEGs.