  Models with an orbifolded universal extra dimension receive important
loop-induced corrections to the masses and couplings of Kaluza-Klein (KK)
particles. The dominant contributions stem from so-called boundary terms which
violate KK number. Previously, only the parts of these boundary terms
proportional to $\ln(\Lambda R)$ have been computed, where $R$ is the radius of
the extra dimension and $\Lambda$ is cut-off scale. However, for typical values
of $\Lambda R \sim 10 \cdots 50$, the logarithms are not particularly large and
non-logarithmic contributions may be numerically important. In this paper,
these remaining finite terms are computed and their phenomenological impact is
discussed. It is shown that the finite terms have a significant impact on the
KK mass spectrum. Furthermore, one finds new KK-number violating interactions
that do not depend on $\ln(\Lambda R)$ but nevertheless are non-zero. These
lead to new production and decay channels for level-2 KK particles at
colliders.
