In this paper we describe an algorithm for accurately segmenting the individual cytoplasm and nuclei from a clump of overlapping cervical cells. Current methods cannot undertake such a complete segmentation due to the challenges involved in delineating cells with severe overlap and poor contrast. Our approach initially performs a scene segmentation to highlight both free-lying cells, cell clumps and their nuclei. Then cell segmentation is performed using a joint level set optimization on all detected nuclei and cytoplasm pairs. This optimisation is constrained by the length and area of each cell, a prior on cell shape, the amount of cell overlap and the expected gray values within the overlapping regions. We present quantitative nuclei detection and cell segmentation results on a database of synthetically overlapped cell images constructed from real images of free-lying cervical cells. We also perform a qualitative assessment of complete fields of view containing multiple cells and cell clumps.