According to Tzouvaras, a set is nontypical in the Russell sense if it belongs to a countable ordinal definable set. The class
H
N
T
\mathbf {HNT}
of all hereditarily nontypical sets satisfies all axioms of
Z
F
\mathbf {ZF}
and the double inclusion
H
O
D
⊆
H
N
T
⊆
V
\mathbf {HOD}\subseteq \mathbf {HNT}\subseteq \mathbf {V}
holds. Several questions about the nature of such sets, recently proposed by Tzouvaras, are solved in this paper. In particular, a model of
Z
F
C
\mathbf {ZFC}
is presented in which
H
O
D
⫋
H
N
T
⫋
V
\mathbf {HOD}\subsetneqq \mathbf {HNT}\subsetneqq \mathbf {V}
, and another model of
Z
F
C
\mathbf {ZFC}
in which
H
N
T
\mathbf {HNT}
does not satisfy the axiom of choice.