The spectrum of heavy-quark hybrids is studied in the leading Born-Oppenhei
mer (LBO) approximation and using leading-order NRQCD simulations with an i
mproved gluon action on anisotropic lattices. The masses of four hybrid sta
tes are obtained from our simulations for lattice spacings 0.1 fm and 0.2 f
m and are compared to the LBO predictions obtained using previously-determi
ned glue-excited static potentials. The consistency of results from the two
approaches reveals a compelling physical picture for heavy-quark hybrid st
ates.