  We compute the dominant new physics contributions to the processes Z -> b b
and B - B in the context of two representative models with extra dimensions.
The main thrust of the calculations focuses on how to control the effects of
the infinite tower of Kaluza-Klein modes inside the relevant one-loop diagrams.
By comparing the results with the existing experimental data, most importantly
those for Rb, we show that one may derive interesting lower bounds on the size
of the compactification scale Mc.
