  An alternative to commonly used domain wall fermions is presented. Some
rigorous bounds on the condition number of the associated linear problem are
derived. On the basis of these bounds and some experimentation it is argued
that domain wall fermions will in general be associated with a condition number
that is of the same order of magnitude as the {\it product} of the condition
number of the linear problem in the physical dimensions by the inverse bare
quark mass. Thus, the computational cost of implementing true domain wall
fermions using a single conjugate gradient algorithm is of the same order of
magnitude as that of implementing the overlap Dirac operator directly using two
nested conjugate gradient algorithms. At a cost of about a factor of two in
operation count it is possible to make the memory usage of direct
implementations of the overlap Dirac operator independent of the accuracy of
the approximation to the sign function and of the same order as that of
standard Wilson fermions.
