According to the thermodynamic model, a very high supersaturation of a solution (up to the complete thermodynamic forbiddenness of crystallization) can be achieved in small-volume systems with phase transitions of the solution-crystal type. Observations in favor of these regularities are described. In particular, "non-Ostwald" behavior in an ensemble of droplets of femto- and picoliter volume is demonstrated: the evaporation and crystallization times of small droplets significantly exceed the evaporation time of large droplets. It is shown experimentally that this behavior is characteristic of different crystals. The described regularities are proposed to have a general character.