  We classify the asymptotic charges of a class of polyhomogeneous
asymptotically-flat spacetimes with finite shear, generalising recent results
on smooth asymptotically-flat spacetimes. Polyhomogenous spacetimes are a
formally consistent class of spacetimes that do not satisfy the well-known
peeling property. As such, they constitute a more physical class of
asymptotically-flat spacetimes compared to the smooth class. In particular, we
establish that the generalised conserved non-linear Newman-Penrose charges that
are known to exist for such spacetimes are a subset of asymptotic BMS charges.
