  Let $Q$ and $Q'$ be two monomial primary ideals of a polynomial algebra $S$
over a field. We give an upper bound for the Stanley depth of $S/(Q\cap Q')$
which is reached if $Q$,$Q'$ are irreducible. Also we show that Stanley's
Conjecture holds for $Q_1\cap Q_2$, $S/(Q_1\cap Q_2\cap Q_3)$, $(Q_i)_i$ being
some irreducible monomial ideals of $S$.

Commutative Algebra