  For a certain class of algebras $\cal A$ we give a method for constructing
Banach spaces $X$ such that every operator on $X$ is close to an operator in
$\cal A$. This is used to produce spaces with a small amount of structure. We
present several applications. Amongst them are constructions of a new prime
Banach space, a space isomorphic to its subspaces of codimension two but not to
its hyperplanes and a space isomorphic to its cube but not to its square.
