  We present a method for the direct extraction of rational contributions to
one-loop scattering amplitudes, missed by standard four-dimensional unitarity
techniques. We use generalised unitarity in $D=4-2\e$ dimensions to write the
loop amplitudes in terms of products of massive tree amplitudes. We find that
the rational terms in $4-2\e$ dimensions can be determined from quadruple,
triple and double cuts without the need for independent pentagon contributions
using a massive integral basis. The additional mass-dependent integral
coefficients may then be extracted from the large mass limit which can be
performed analytically or numerically. We check the method by computing the
rational parts of all gluon helicity amplitudes with up to six external legs.
We also present a simple application to amplitudes with external massless
fermions.
