  We construct eight-stack intersecting D5-brane models, with an orbifold
transverse space, that yield the (non-supersymmetric) standard model up to
vector-like leptons. The matter includes right-chiral neutrinos and the models
have the renormalisable Yukawa couplings to tachyonic Higgs doublets needed to
generate mass terms for {\it all} matter, including the vector-like leptons.
The models are constrained by the requirement that twisted tadpoles cancel,
that the gauge boson coupled to the weak hypercharge $U(1)_Y$ does not get a
string-scale mass via a generalised Green-Schwarz mechanism, and that there are
no surviving, unwanted gauged U(1) symmetries coupled to matter.
  Gauge coupling constant ratios close to those measured are easily obtained
for reasonable values of the parameters, consistently with having the string
scale close to the electroweak scale, as required to avoid the hierarchy
problem. Unwanted (colour-triplet, charged-singlet, and neutral-singlet) scalar
tachyons can be removed by a suitable choice of the parameters.
