Because ice-I is less dense than water, the formation of an ice nucleus in an isochoric (constant volume) chamber will cause an increase in pressure. This analysis shows that the energy required to overcome such a pressure increase makes homogeneous ice nucleation thermodynamically improbable in an isochoric system at temperatures above -109 degrees C. By suppressing ice nucleation, isochoric cooling is expected to significantly promote vitrification. Because water has a higher freezing temperature and a lower glass-transition temperature than physiological solutions, this analysis represents a scenario for avoiding ice crystallization during the preservation of biological substances. While isochoric cryopreservation has not yet been put into practice, this theoretical, first-order analysis suggests that if attainable it could make organ preservation significantly more effective and practical.