  We generalize the approach to localization in one dimension introduced by
Kunz-Souillard, and refined by Delyon-Kunz-Souillard and Simon, in the early
1980's in such a way that certain correlations are allowed. Several
applications of this generalized Kunz-Souillard method to almost periodic
Schr\"odinger operators are presented.
  On the one hand, we show that the Schr\"odinger operators on
$l^2(\mathbb{Z})$ with limit-periodic potential that have pure point spectrum
form a dense subset in the space of all limit-periodic Schr\"odinger operators
on $l^2(\mathbb{Z})$. More generally, for any bounded potential, one can find
an arbitrarily small limit-periodic perturbation so that the resulting operator
has pure point spectrum. Our result complements the known denseness of
absolutely continuous spectrum and the known genericity of singular continuous
spectrum in the space of all limit-periodic Schr\"odinger operators on
$l^2(\mathbb{Z})$.
  On the other hand, we show that Schr\"odinger operators on $l^2(\mathbb{Z})$
with arbitrarily small one-frequency quasi-periodic potential may have pure
point spectrum for some phases. This was previously known only for
one-frequency quasi-periodic potentials with $\|\cdot\|_\infty$ norm exceeding
$2$, namely the super-critical almost Mathieu operator with a typical frequency
and phase. Moreover, this phenomenon can occur for any frequency, whereas no
previous quasi-periodic potential with Liouville frequency was known that may
admit eigenvalues for any phase.
