Non-cupping and randomness

Let $Y \in \Delta^0_2$ be Martin-Löf-random. Then there is a promptly simple set $A$ such that for each Martin-Löf-random set $Z$, $Y \le_T A \oplus Z \Rightarrow Y \le_T Z$. When $Y = \Omega$, one obtains a c.e. non-computable set $A$ which is not weakly Martin-Löf cuppable. That is, for any Martin-Löf-random set $Z$, if $\emptyset' \le_T A \oplus Z$, then $\emptyset' \le_T Z$.