  Let $R$ be a commutative ring with identity. The small finitistic dimension
$fPD(R)$ of $R$ is defined to be the supremum of projective dimensions of
$R$-modules with finite projective resolutions. In this paper, we characterize
a ring $R$ with $fPD(R)\leq n$ using finitely generated semi-regular ideals,
tilting modules or vaguely associated prime ideals. As an application, we
obtain that if $R$ is a Noetherian ring, then $fPD(R)= \sup\{grade(m,R)|m\in
Max(R)\}$ where $grade(m,R)$ is the grade of $m$ on $R$ . We also show that a
ring $R$ satisfies $fPD(R)\leq 1$ if and only if $R$ is a $DW$ ring.
