  It has been recently proposed that we might live in a universe with a single
compact extra dimension, whose mesoscopic size is dictated by the measured
value of the cosmological constant. Central to this proposal is the result that
in a $4+n$ dimensional theory with $n$ compact dimensions a tower of
Kaluza-Klein (KK) states contributes an amount $m_{_{\rm KK}}^4$ to the vacuum
energy $\rho_4$, where $m_{_{\rm KK}}$ is the KK scale of the tower. We show
that the result $\rho_4 \sim m_{_{\rm KK}}^4$ comes from a mistreatment of the
asymptotics of the loop momenta in the $4+n$ original theory. When the latter
are correctly treated, new UV-sensitive terms appear in $\rho_4$ that
invalidate the prediction of the dark dimension. We also show that, despite
recent claims to the contrary, it is always possible to perform consistent
effective field theory calculations that include only a finite number of tower
states.
