One of the major trends in primate evolution generally and hominid evolution in particular, is cranio-facial contraction accompanied by an increase in cranial capacity. Landmark-based morphometric methods are applied to adult skulls of great apes (Gorilla, Pan), australopithecines (Australopithecus and Paranthropus), and humans (Homo eragster, erectus, neanderthalensis, and sapiens). Morphological changes quantified by vector fields (Procrustes methods) indicate that these skull plans are characterized by distinctive degrees of cranio-facial contraction. These suggest the existence of three discrete skull organization plans: "great ape", "australopithecine" and "Homo". This paper focuses on the "Homo" skull bauplan and discusses the possible relationships between greatly increased cranial capacity and preeclampsia. The earliest species of the human lineage exhibit less cranio-facial contraction and smaller cranial capacity than Homo neanderthalensis and modern Homo sapiens. Neandertalization introduces a posterior elongation of the skull and leads to a large increase in cranial capacity in the last Neandertals, with values as large as in present-day H. sapiens. Consequently, a new biological hypothesis is proposed to account for the unexplained disappearance of H. neanderthalensis some 30000 years ago related to the possible appearance of preeclampsia as a factor affecting the survival of the species.