  We study bounded width algebras which are minimal in the sense that every
proper reduct does not have bounded width. We show that minimal bounded width
algebras can be arranged into a pseudovariety with one basic ternary operation.
We classify minimal bounded width algebras which have size at most three, and
prove a structure theorem for minimal bounded width algebras which have no
majority subalgebra, which form a pseudovariety with a commutative binary
operation. As a byproduct of our results, we also classify minimal clones which
have a Taylor term.
