  In 2001, Zurek derived the generic minimum scale $a_{Z}$ for the area of
structures of Wigner's quantum phase distribution. Here we show by
construction, using superoscillatory functions, that the Wigner distribution
can locally show regular spotty structures on scales much below Zurek's scale
$a_{Z}$. The price to pay for the presence of such structures is their
exponential smallness. For the case we construct there is no increased
interferometric sensitivity from the presence of patches with superoscillatory
structure in phase-space.
