  Transverse-momentum cuts on undistinguished particles in two-body final
states induce an enhanced sensitivity to low momentum scales. This undesirable
feature, which ultimately leads to an instability of the fixed-order series,
poses additional challenges to non-local subtraction schemes. In this letter,
we address this issue for general colour-singlet processes within the
$q_T$-subtraction formalism, focussing on neutral-current Drell-Yan production.
We present a simple procedure to reduce the dependence on the slicing parameter
from linear to quadratic, by accounting for the linear power corrections
through an appropriate recoil prescription. We observe a dramatical improvement
of the numerical convergence and a reduction of the systematic uncertainties.
We also discuss how a linear dependence in $q_T$ can be avoided for Drell-Yan
production by using staggered cuts, which, to the best of our understanding,
could be used in experimental analyses. We show that our approach can be
successfully applied also to on-shell $ZZ$ production. We finally study
diphoton production and verify that our approach is insufficient to capture the
linear power corrections introduced by the isolation procedure. The recoil
prescription is available in version 2.1 of MATRIX.
