  L-spaces were introduced by Ozsvath and Szabo using the Heegaard Floer
Homology. In the quest for L-spaces we consider links of isolated complete
intersection surface singularities. We show that if such a manifold is an
L-space, then it is a link of a rational singularity. We also prove that if it
is not an L-space then it admits a symplectic filling with $b_2^+>0$. Based on
these results we pin down all integral homology sphere L-spaces in this realm.
