  We present three families of minimal border rank tensors: they come from
highest weight vectors, smoothable algebras, or monomial algebras. We analyse
them using Strassen's laser method and obtain an upper bound $2.431$ on
$\omega$. We also explain how in certain monomial cases using the laser method
directly is less profitable than first degenerating. Our results form possible
paths in the search for valuable tensors for the laser method away from
Coppersmith-Winograd tensors.
