  We study a recently-proposed approach to the numerical evaluation of
multi-loop Feynman integrals using available sector decomposition programs. As
our main example, we consider the two-loop integrals for the $\alpha \alpha_s$
corrections to Drell-Yan lepton production with up to one massive vector boson
in physical kinematics. As a reference, we evaluate these planar and non-planar
integrals by the method of differential equations through to weight five.
Choosing a basis of finite integrals for the numerical evaluation with SecDec3
leads to tremendous performance improvements and renders the otherwise
problematic seven-line topologies numerically accessible. As another example,
basis integrals for massless QCD three loop form factors are evaluated with
FIESTA4. Here, employing a basis of finite integrals results in an overall
speedup of more than an order of magnitude.
