  We propose a simple formula for the 4d-2d partition function of half-BPS
surface defects in $d=4,\ \mathcal{N}=2$ gauge theories:
$Z^{\text{4d-2d}}=\langle Z^{\text{2d}} \rangle_{\text{4d}}$. Our results are
applicable for any surface defect obtained by gauging a 2d flavour symmetry
using a 4d gauge group. For defects obtained via the Higgsing procedure, our
formula reproduces the recent calculation by Pan and Peelaers. For Gukov-Witten
defects our results reproduce the orbifold calculation by Kanno and Tachikawa.
We emphasize the role of "negative vortices" which are realized as negative D0
branes.
