Our earlier arguments (Berry M V and Robbins J M 1997 Proc. R. Soc. Lond. A
453 1771-90) leading to the spin-statistics relation are summarized and th
en revisited. Constructions are described that satisfy all our previous req
uirements but lead to the wrong exchange sign (one such alternative is the
replacement of commutators by anticommutators in the Schwinger representati
on of the spins of the particles); we suggest why these might be unacceptab
le.