Mixtures of various ratios of cubic ice and glassy water were obtained by so-called hyperquenching of micrometer-sized water droplets at cooling rates of ≈106–107 K s−1 on a substrate held at selected temperatures between 130 and 190 K. These samples were characterized by differential scanning calorimetry (DSC) and X-ray diffraction. The minimum deposition temperature to obtain almost entirely vitrified samples is ≈140 K. Glassy water prepared at this temperature exhibits on heating an endothermic step assignable to a glass→liquid transition, without the requirement for previous annealing. Cubic ice samples obtained by deposition at 160 and 170 K undergo on heating two distinct exothermic processes of comparable intensity. One centered at ≈230 K is caused by the phase transition to hexagonal ice. The other is centered at ≈201 K in a sample deposited at 170 K, and it shifts to ≈193 K on deposition at 160 K. The latter process is attributed to the increase in particle size, relief of non-uniform strain and/or healing of different kinds of defects. Since the temperature of this second exotherm depends on the deposition temperature of the sample, it merges on sample deposition at 190 K with the exotherm from the cubic→hexagonal ice phase transition. Therefore, this can lead to an overestimation of the heat of the cubic→hexagonal phase transition. For samples deposited at 150 K, the low temperature exotherm merges with the intense exotherm due to glassy water→cubic ice phase transition. X-ray diffractograms and DSC scans of cubic ice samples of different thermal history show, after annealing at the same temperature of 183 K for 5 min, essentially identical patterns. Likewise, X-ray diffractograms of cubic ice made on heating hyperquenched glassy water or vapor-deposited amorphous solid water up to 183 K are indistinguishable. Cubic ice deposited at 190 K, or annealed at 183 K, contains at most 20% amorphous component which persists up to the cubic to hexagonal ice phase transition. This is in contrast to recent claims of Jenniskens et al. (J. Chem. Phys. 1997, 107, 1232) that cubic ice obtained by heating thin films of vapor-deposited amorphous water contains more than 50% of amorphous, or even liquid, water.