  We show that one can force over $L$ that $\Sigma^1_3$-separation holds, while
$\Pi^1_3$-reduction fails, thus separating these two principles for the first
time. The construction can be lifted to canonical inner models $M_n$ with
$n$-many Woodin cardinals, yielding that assuming the existence of $M_n$,
$\Sigma^1_{n+3}$-separation can hold, yet $\Pi^1_{n+3}$-reduction fails.
