The reversible phase transition from hydrochloric-acid-doped ice VI to its hydrogen-ordered counterpart ice XV is followed using differential scanning calorimetry. Upon cooling at ambient pressure fast hydrogen ordering is observed at first followed by a slower process which manifests as a tail to the initial sharp exotherm. The residual hydrogen disorder in H2O and D2O ice XV is determined as a function of the cooling rate. We conclude that it will be difficult to obtain fully hydrogen-ordered ice XV by cooling at ambient pressure. Our new experimental findings are discussed in the context of recent computational work on ice XV. (C) 2015 Elsevier B.V. All rights reserved.