  Large logarithms that arise in cross sections due to the collinear and soft
singularities of QCD are traditionally treated using parton showers or analytic
resummation. Parton showers provide a fully-differential description of an
event but are challenging to extend beyond leading logarithmic accuracy. On the
other hand, resummation calculations can achieve higher logarithmic accuracy
but often for only a single observable. Recently, there have been many
resummation calculations that jointly resum multiple logarithms. Here we
investigate the benefits and limitations of joint resummation in a case study,
focussing on the family of $e^+e^-$ event shapes called angularities. We
calculate the cross section differential in n angularities at next-to-leading
logarithmic accuracy. We investigate whether reweighing a flat phase-space
generator to this resummed prediction, or the corresponding distributions from
Herwig and Pythia, leads to improved predictions for other angularities. We
find an order of magnitude improvement for n = 2 over n = 1, highlighting the
benefit of joint resummation, but diminishing returns for larger values of n.
