  For any $d\ge 4$, by deformation theory of schemes, we present examples of
(complete or excellent) $d$-dimensional mixed characteristic normal local
domains admitting no small Cohen-Macaulay algebra, but admitting instances of
small (maximal) Cohen-Macaulay modules. It is also shown that a graded normal
domain over a field whose Proj is an Abelian variety admits a graded small
(maximal) Cohen-Macaulay module.
