In this paper we determine the possible Hilbert functions of
a Cohen--Macaulay local ring of dimension $d$ and
multiplicity $e$, in the case where the embedding dimension
$v$ satisfies $v=e+d-3$ and the Cohen--Macaulay type
is less than or equal to $e-3$.
1991 Mathematics Subject Classification: primary 13D40;
secondary 13P99.