  Standard dipole parton showers are known to yield incorrect subleading-colour
contributions to the leading (double) logarithmic terms for a variety of
observables. In this work, concentrating on final-state showers, we present two
simple, computationally efficient prescriptions to correct this problem,
exploiting a Lund-diagram type classification of emission regions. We study the
resulting effective multiple-emission matrix elements generated by the shower,
and discuss their impact on subleading colour contributions to leading and
next-to-leading logarithms (NLL) for a range of observables. In particular we
show that the new schemes give the correct full colour NLL terms for global
observables and multiplicities. Subleading colour issues remain at NLL (single
logarithms) for non-global observables, though one of our two schemes
reproduces the correct full-colour matrix-element for any number of
energy-ordered commensurate-angle pairs of emissions. While we carry out our
tests within the PanScales shower framework, the schemes are sufficiently
simple that it should be straightforward to implement them also in other shower
frameworks.
