  In a paper from 2001 (Journal of the LMS), Diestel and Leader offered a proof
that a connected graph has a normal spanning tree if and only if it does not
contain a minor from two specific forbidden classes of graphs, all of
cardinality $\aleph_1$. Unfortunately, their proof contains a gap, and their
result is incorrect. In this paper, we construct a third type of obstruction:
an $\aleph_1$-sized graph without a normal spanning tree that contains neither
of the two types described by Diestel and Leader as a minor. Further, we show
that any list of forbidden minors characterising the graphs with normal
spanning trees must contain graphs of arbitrarily large cardinality.
