  The listsize capacity of a discrete memoryless channel is the largest
transmission rate for which the expectation---or, more generally, the $\rho$-th
moment---of the number of messages that could have produced the output of the
channel approaches one as the blocklength tends to infinity. We show that for
channels with feedback this rate is upper-bounded by the maximum of Gallager's
$E_0$ function divided by $\rho$, and that equality holds when the zero-error
capacity of the channel is positive. To establish this inequality we prove that
feedback does not increase the cutoff rate. Relationships to other notions of
channel capacity are explored.
