  The elementary and solitonic supersymmetric $p$-brane solutions to
supergravity theories form families related by dimensional reduction, each
headed by a maximal (`stainless') member that cannot be isotropically
dimensionally oxidized into higher dimensions. We find several new families,
headed by stainless solutions in various dimensions $D\le 9$. In some cases,
these occur with dimensions $(D,p)$ that coincide with those of descendants of
known families, but since the new solutions are stainless, they are necessarily
distinct. The new stainless supersymmetric solutions include a 6-brane and a
5-brane in $D=9$, a string in $D=5$, and particles in all dimensions $5\le D\le
9$.
