  The small finitistic dimension $\fPD(R)$ of a ring $R$ is defined to be the
supremum of projective dimensions of $R$-modules with finite projective
resolutions. In this paper, we investigate the small finitistic dimensions of
four types of ring constructions: polynomial rings, formal power series rings,
trivial extensions and amalgamations. Besides, we show the small finitistic
dimensions of a ring is less than or equal to its Krull dimension. We also give
a total ring of quotients with infinite small finitistic dimension.
