  We prove that the spectrum of a limit-periodic Schr\"odinger operator is
homogeneous in the sense of Carleson whenever the potential obeys the
Pastur--Tkachenko condition. This implies that a dense set of limit-periodic
Schr\"odinger operators have purely absolutely continuous spectrum supported on
a homogeneous Cantor set. When combined with work of Gesztesy--Yuditskii, this
also implies that the spectrum of a Pastur--Tkachenko potential has infinite
gap length whenever the potential fails to be uniformly almost periodic.
