  It is proved that given any prime ideal $\mathfrak{p}$ of height at least 2
in a countable commutative noetherian ring $A$, there are uncountably many more
dualizable objects in the $\mathfrak{p}$-local $\mathfrak{p}$-torsion stratum
of the derived category of $A$ than those that are obtained as retracts of
images of perfect $A$-complexes. An analogous result is established dealing
with the stable module category of the group algebra, over a countable field of
positive characteristic $p$, of an elementary abelian $p$-group of rank at
least 3.
