  We show that if $cf(2^{\aleph_0})=\aleph_1,$ then any non-trivial
$\aleph_1$-closed forcing notion of size $\leq 2^{\aleph_0}$ is forcing
equivalent to $Add(\aleph_1, 1),$ the Cohen forcing for adding a new Cohen
subset of $\omega_1.$ We also produce, relative to the existence of suitable
large cardinals, a model of $ZFC$ in which $2^{\aleph_0}=\aleph_2$ and all
$\aleph_1$-closed forcing notion of size $\leq 2^{\aleph_0}$ collapse
$\aleph_2,$ and hence are forcing equivalent to $Add(\aleph_1, 1).$ These
results answer a question of Scott Williams from 1978. We also extend a result
of Todorcevic and Foreman-Magidor-Shelah by showing that it is consistent that
every partial order which adds a new subset of $\aleph_2,$ collapses $\aleph_2$
or $\aleph_3.$
