  Let X_n := \bar M_{0,n}, the moduli space of n-pointed stable genus zero
curves, and let X_{n,m} be the quotient of X_n by the action of the symmetric
group S_{n-m} on the last n-m marked points. The cones of effective divisors of
X_{n,m}, m = 0,1,2, are calculated. Using this, upper bounds for the cones
Mov(X_{n,m}) generated by divisors with moving linear systems are calculated, m
= 0,1, along with the induced bounds on the cones of ample divisors of \bar M_g
and \bar M_{g,1}. As an application, the cone of effective divisors of \bar
M_{2,1} is analyzed in detail.
