  In this paper I reconsider the use of the left ideals of the even-grade
subalgebra of spacetime algebra to describe fermionic excitations. When
interpreted as rotors the general elements of an even-grade left-ideal describe
massless particles in chiral flavour doublets. To study the application of
these ideas to the standard Dirac formalism I construct a $2 \times 2$-matrix
representation with bivector insertions for the Dirac algebra. This algebra has
four ideals, and this approach clarifies how the identification of Dirac
$\g_{\mu}$-matrices with orthonormal basisvectors ${\bf e}_{\nu}$ annihilates
half of the ideals. For one possible choice of this mapping the remaining
ideals the chiral left- and righthanded components of the fermion coincide with
the even- and odd elements of spacetime algebra.
