  We prove a generalization of the author's work to show that any subset of the
primes which is `well-distributed' in arithmetic progressions contains many
primes which are close together. Moreover, our bounds hold with some uniformity
in the parameters. As applications, we show there are infinitely many intervals
of length $(\log{x})^{\epsilon}$ containing $\gg_\epsilon \log\log{x}$ primes,
and show lower bounds of the correct order of magnitude for the number of
strings of $m$ congruent primes with $p_{n+m}-p_n\le \epsilon\log{x}$.
