K E Y w ORDS. Cryoquenchant, propane, freeze substitution, Freon 22, ice crystal damage, cooling rates. SUMMARY Three .approaches were taken with the aim of defining the optimum conditions for rapid cryopreservation in liquid quenchants. In a theoretical approach, two mathematical models were used. The first is of value in defining the absolute maximum rates of cooling which could be achieved at various depths in the tissues. The second highlights the poor thermal properties of liquid coolants and therefore emphasizes the essential requirement for vigorous quenchant mixing and rapid specimen entry.Experimental work with thermocouples showed that fastest cooling rates occur at the leading edge of the object entering coolant. Of five liquid quenchants investigated, cooling rates were in the order, propane > Freon 22 > Freon 12 > liquid nitrogen slush > liquid nitrogen. Other considerations, however, may affect the choice of quenchant. For a given quenchant, cooling rate is maximal near the equilibrium freezing point. The consequences of quenching in the presence of thermal gradients either within the coolant or in the gas layer above it are shown. Cooling rate was found to be approximately proportional to entry velocity at least up to N 2 m s-1 in our system. Stereological analysis of rapidly quenched, freeze-substituted tissue samples, of geometry which imposed an approximately unidirectional heat flow, revealed four zones : (i) a narrow surface layer ( N 10 pm) of low image contrast and apparent absence of ice crystals; (ii) a zone of enhanced contrast with ice crystals whose size increased rapidly with depth from the surface (the 'slope'); (iii) a sharply defined zone (the 'ridge') of maximum ice crystal size beyond which there is (iv) an extensive 'plateau' with smaller ice crystals and no marked increase in size with depth. The 'ridge' of maximal ice-crystal damage was consistently found but varied considerably in depth from the surface ( N 25-120 pm) between samples. The existence of the deeper plateau region of relatively uniform ice-crystal-size may be of significance in X-ray microanalytical studies of physiological processes at some depth from the sample surface.In terms of our present understanding of the quenching process, the conditions for optimal cryofixation of small tissue samples are listed.