  The notion of slicely countably determined (SCD) sets was introduced in 2010
by A.~Avil\'{e}s, V.~Kadets, M.~Mart\'{i}n, J.~Mer\'{i} and V.~Shepelska. We
solve in the negative some natural questions about preserving being SCD by the
operations of union, intersection and Minkowski sum. Moreover, we demonstrate
that corresponding examples exist in every space with the Daugavet property and
can be selected to be unit balls of some equivalent norms. We also demonstrate
that almost SCD sets need not be SCD, thus answering a question posed by A.
Avil\'{e}s et al.
