In previous work, water's second glass transition was investigated based on an amorphous sample made from crystalline ice (Amann-Winkel et al., Proc. Natl. Acad. Sci. U.S.A. 110 (44) 17720-17725). In the present work, we investigate water's second glass transition based on the genuine glassy state of high-density water as prepared from micron-sized liquid water droplets, avoiding crystallinity at all stages. All the calorimetric features of water's second glass transition observed in the

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... s work are also observed here on the genuine glassy samples. This suggests that the glass transition indeed thermodynamically links amorphous ices continuously with deeply supercooled water. We proceed to extend the earlier study by investigating the effect of preparation history on the calorimetric glass transition temperature. The best samples prepared here feature both a lower glass transition temperature Tg,2 and a higher polyamorphic transition temperature Tons, thereby extending the range of thermal stability in which the deeply supercooled liquid can be observed by about 4 K. Just before the polyamorphic transition, we observe a spike-like increase of heat capacity that we interpret in terms of nucleation of low-density water. Without this spike, the width of water's second glass transition is 15 K, and the Δcp amounts to 3{plus minus}1 J K-1 mol-1, making the case for HDL being a strong liquid. We suggest that samples annealed at 1.9 GPa to 175 K and decompressed at 140 K to {greater than or equal to}0.10 GPa are free from such nuclei and represent the most ideal HDA glasses.