  We revisit the calculation of the relic density of the lightest Kaluza-Klein
particle (LKP) in the model of Universal Extra Dimensions. The Kaluza-Klein
(KK) particle spectrum at level one is rather degenerate, and various
coannihilation processes may be relevant. We extend the calculation of
hep-ph/0206071 to include coannihilation processes with all level one KK
particles. In our computation we consider a most general KK particle spectrum,
without any simplifying assumptions. In particular, we do not assume a
completely degenerate KK spectrum and instead retain the dependence on each
individual KK mass. As an application of our results, we calculate the
Kaluza-Klein relic density in the Minimal UED model, turning on coannihilations
with all level one KK particles. We then go beyond the minimal model and
discuss the size of the coannihilation effects separately for each class of
level 1 KK particles. Our results provide the basis for consistent relic
density computations in arbitrarily general models with Universal Extra
Dimenions.
