  We show there exists a complete theory in a language of size continuum
possessing a unique atomic model which is not constructible. We also show it is
consistent with $ZFC + \aleph_1 < 2^{\aleph_0}$ that there is a complete theory
in a language of size $\aleph_1$ possessing a unique atomic model which is not
constructible. Finally we show it is consistent with $ZFC + \aleph_1 <
2^{\aleph_0}$ that for every complete theory $T$ in a language of size
$\aleph_1$, if $T$ has uncountable atomic models but no constructible models,
then $T$ has $2^{\aleph_1}$ atomic models of size $\aleph_1$.
