A complete description of the non-dynamical r-matrices of the degenerate
Calogero-Moser models based on $gl_n$ is presented. First the most general
momentum independent r-matrices are given for the standard Lax representation
of these systems and those r-matrices whose coordinate dependence can be gauged
away are selected. Then the constant r-matrices resulting from gauge
transformation are determined and are related to well-known r-matrices. In the
hyperbolic/trigonometric case a non-dynamical r-matrix equivalent to a
real/imaginary multiple of the Cremmer-Gervais classical r-matrix is found. In
the rational case the constant r-matrix corresponds to the antisymmetric
solution of the classical Yang-Baxter equation associated with the Frobenius
subalgebra of $gl_n$ consisting of the matrices with vanishing last row. These
claims are consistent with previous results of Hasegawa and others, which imply
that Belavin's elliptic r-matrix and its degenerations appear in the
Calogero-Moser models. The advantages of our analysis are that it is elementary
and also clarifies the extent to which the constant r-matrix is unique in the
degenerate cases.