  We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with
all positive helicities in compact analytic form using D-dimensional local
integrands that are free of spurious singularities. The integrand is fixed from
on-shell tree amplitudes in six dimensions using D-dimensional generalised
unitarity cuts. The resulting expressions are shown to have manifest infrared
behaviour at the integrand level. We also find simple representations of the
rational terms obtained after integration in 4-2epsilon dimensions.
