  In Koeller \cite{koerprops} the twelve variants of the Reifenberg properties
known to be instrumental in the theory of minimal surfaces were classified with
respect to various Hausdorff measure based measure theoretic properties. The
classification lead to the consideration of fine geometric properties and a
connection to fractal geometry. The current work develops this connection and
extends the classification to consider Minkowski-dimension, packing dimension,
measure, and rectifiability, and the equality of packing and Hausdorff measures
with interesting results.
