  Unphysical 3-form flux singularities near anti-branes have been argued to get
resolved in the classical supergravity regime when brane polarisation is
properly taken into account. The only example that does not seem to fit this
logic is the $\bar{\text{D6}}$-brane because of a no-go theorem for well
behaved supergravity solutions with negative D6 charge. In this paper we first
review the existing results demonstrating how brane polarisation resolves
singularities for $\bar{\text{D3}}$-branes and then we improve on the
description of the polarisation of $\bar{\text{D6}}$-branes into KK5 dipoles.
We argue that the meta-stable state carries exactly zero (anti-)D6 charge,
which is the unique way around the no-go theorem. We then provide numerical
evidence for well-behaved solutions that describe such meta-stable states.
