In [17] the authors showed the existence of subsets
![$S\subset
{\mathbb{C}}$](img3.png)
with 7 elements such that if a non-constant meromorphic
function
![$f,$](img4.png)
having finitely many poles, and an
![$L$](img2.png)
-function in
the Selberg class share
![$S$](img5.png)
CM, then
![$f=L.$](img6.png)
In this paper, we
present a class of such subsets
![$S$](img5.png)
with 5 elements. Moreover, when
avoiding the hypothesis of having finitely many poles, we show a
class of such subsets
![$S$](img5.png)
with
![$9$](img7.png)
elements.