  Let $K$ be a field and $I$ a monomial ideal of the polynomial ring
$S=K[x_1,\ldots, x_n]$. We show that if either: 1) $I$ is almost complete
intersection, 2) $I$ can be generated by less than four monomials; or 3) $I$ is
the Stanley-Reisner ideal of a locally complete intersection simplicial complex
on $[n]$, then Stanley's conjecture holds for $S/I$.
