  We find for g at most 5 a stratification of depth g-2 of the moduli space of
curves M_g with the property that its strata are affine and the classes of
their closures provide a Q-basis for the Chow ring of M_g. The first property
confirms a conjecture of one of us. The way we establish the second property
yields new (and simpler) proofs of theorems of Faber and Izadi which, taken
together, amount to the statement that in this range the Chow ring is generated
by the lambda-class.
