High-density amorphous ice (HDA). made by compression of hexagonal ice at 77 K, was heated at a constant pressure of 0.81 GPa up to 195 K and its phase transition followed by displacement-temperature curves. The crystalline phases recovered at 77 K and 1 bar were characterized by X-ray diffraction. Pure D2O ice IV and nearly pure H2O ice IV were formed on slow heating at a rate of approximate to0.4 K min(-1), whereas pure H2O and D2O ice XII were formed on fast heating at greater than or equal to15 K min(-1). On heating HDA at rates inbetween, a mixture of ice IV and ice XII is obtained, where their relative yields depend in a systematic manner on the heating rate. Conversion of HDA into either ice IV or ice XII is an example of a "parallel reaction" where the relative yields of ice IV and ice XII can be controlled by temperature, that is in our approach by the rate of heating. It is conceivable that a similar behavior occurs on crystallization of the related pressure-amorphized silica.