It is shown that, after a resummation of leading high-temperature cont
ributions, a complete and gauge-independent result for the non-Abelian
Debye screening mass at next-to-leading order can be extracted from t
he static gluon propagator. In contrast with previous, incomplete resu
lts, the correction to the Debye mass is found to be logarithmically s
ensitive to the nonperturbative magnetic mass and positive, in accorda
nce with recent high-statistics results from lattice calculations.