  A ring with an involution * is called strongly $J$-*-clean if every element
is a sum of a projection and an element of the Jacobson radical that commute.
In this article, we prove several results characterizing this class of rings.
It is shown that a *-ring $R$ is strongly $J$-*-clean, if and only if $R$ is
uniquely clean and strongly *-clean, if and only if $R$ is uniquely strongly
*-clean, that is, for any $a\in R$, there exists a unique projection $e\in R$
such that $a-e$ is invertible and $ae=ea$.
