  In 2018 Celikbas, Laxmi, Kra\'skiewicz, and Weyman exhibited an interesting
family of perfect ideals of codimension three, with five generators, of
Cohen-Macaulay type two with trivial multiplication on the Tor algebra. All
previously known perfect ideals of codimension three, with five generators, of
Cohen-Macaulay type two had been found by Brown in 1987. Brown's ideals all
have non-trivial multiplication on the Tor algebra. We prove that all of the
ideals of Brown are obtained from the ideals of Celikbas, Laxmi, Kra\'skiewicz,
and Weyman by (non-homogeneous) specialization. We also prove that both
families of ideals, when built using power series variables over a field,
define rigid algebras in the sense of Lichtenbaum and Schlessinger.
