  A valid inequality \alpha^Tx \ge \alpha_0 for a set covering problem is said
to have pitch <= k ( a positive integer) if the k smallest positive \alpha_j
sum to at least alpha_0. This paper presents a new, simple derivation of a
relaxation for set covering problems whose solutions satisfy all valid
inequalities of pitch and is of polynomial size, for each fixed . We also
consider the minimum knapsack problem, and show that for each fixed integer p >
0 and 0 < \epsilon < 1 one can separate, within additive tolerance \epsilon,
from the relaxation defined by the valid inequalities with coefficients in {0,
1, . . . , p} in time polynomial in the number of variables and 1/\epsilon.
