  The aim of the paper is to establish (local) optimal embeddings of Besov
spaces $B^{0,b}_{p,r}$ involving only a slowly varying smoothness $b$. In
general, our target spaces are outside of the scale of Lorentz-Karamata spaces
and are related to small Lebesgue spaces. In particular, we improve results
from [CGO11b], where the targets are (local) Lorentz-Karamata spaces. To derive
such results, we apply limiting real interpolation techniques and weighted
Hardy-type inequalities.
