  We strengthen, in various directions, the theorem of Garnett that every
$\sigma$-compact, completely regular space $X$ occurs as a Gleason part for
some uniform algebra. In particular, we show that the uniform algebra can
always be chosen so that its maximal ideal space contains no analytic discs. We
show that when the space $X$ is metrizable, the uniform algebra can be chosen
so that its maximal ideal space is metrizable as well. We also show that for
every locally compact subspace $X$ of a Euclidean space, there is a compact set
$K$ in some ${\mathbb C}^N$ so that $\hat K \setminus K$ contains a Gleason
part homeomorphic to $X$ and $\hat K$ contains no analytic discs.
