  We present an extension of the renormalisation procedure based on the
R-operation in $D$ dimensions at two-loop level, in which the numerators of all
Feynman diagrams can be constructed in four dimensions, and the rational terms
stemming from the interplay of $(D-4)$-dimensional numerator parts and UV poles
are fully reconstructed from a finite set of universal local counterterms. This
represents an extension of the concept of rational terms of type $R_2$ to two
loops. We provide a general method to compute one and two-loop rational
counterterms from massive one-scale tadpole integrals. Finally, we present the
full set of rational counterterms of UV origin for QED up to two-loop order.
