  We provide an explicit construction of Ricci-flat K3 metrics. It employs the
technology of D-geometry, which in the case of interest is equivalent to a
hyper-K\"ahler quotient. We relate it to the construction of arXiv:1810.10540,
and in particular show that it contains the solution to the BPS state counting
problem (that of computing the BPS index of a heterotic little string theory
compactified on $T^2$) discussed therein, which is the data needed for this
second construction of K3 metrics.
