In the context of the PanScales parton shower project, I describe two advances in the development of
final-state parton showers with controlled logarithmic accuracy. The first (Ref. [1]) involves simple
new algorithms to resolve the long-standing issue of incorrect subleading-colour contributions at
leading logarithmic (LL) accuracy in dipole- and antenna-type final-state showers, and also enables
the PanScales showers to obtain full-colour NLL accuracy for many observables. The second
(Ref. [2]) concerns spin correlations, where we propose a spinor-product based implementation
of the well-established Collins algorithm. We verify the logarithmic accuracy of the results
with separate purely collinear calculations, using novel spin-sensitive jet observables that are of
potential interest also for future experimental measurements.