A major problem in the automation of cervical cytology screening is the segmentation of cell images. This paper describes various standard segmentation methods plus one which determines a segmentation threshold based on the stability of the perimeter of the cell as the threshold is varied. As well as contour, certain structural information is used to decide upon the threshold which separates cytoplasm from the background. Once the cytoplasm threshold is found, cytoplasm and nucleus are separated by simple clustering into three groups, cytoplasm, folded cytoplasm and nucleus. These techniques have been tested on 1500 cervical cells that belong to one of eight normal classes and five abnormal classes. A minimum Mahalanobis distance classifier was used to compare results. Manually thresholded cells were classified correctly 66.0% of the time for the 13 class problem and 95.2% of the time on the two (normal-abnormal) class problem. The contour tracing technique was 52.9% and 90.0% correct, respectively.