Abstract: We consider higher-order QCD corrections to the production of high-mass systems in hadron collisions within the transverse-momentum (q(T)) subtraction formalism. We present amethod to consistently remove the linear power corrections in q(T) which appears when fiducial kinematical cuts are applied on the final state system. We consider explicitly the case of fiducial cross sections for Drell-Yan lepton pair production at the Large Hadron Collider up to next-to-nextto-next-to-leading order (N3LO) in QCD. We have implemented our method within the DYTurbo numerical program and we have obtained perturbative predictions which are in agreement at the permille level with those obtained with local subtraction formalisms up to the next-to-next-toleading order (NNLO). At the N3LO we are able to provide predictions for fiducial cross sections with numerical accuracy at the permille level.