  The Riemann Hypothesis (RH) - that all nonreal zeros of Riemann's zeta
function shall have real part 1/2 - remains a major open problem. Its most
concrete equivalent is that an infinite sequence of real numbers, the
Keiper--Li constants, shall be everywhere positive (Li's criterion). But those
numbers are analytically elusive and strenuous to compute, hence we seek
simpler variants. The essential sensitivity to RH of that sequence lies in its
asymptotic tail; then, retaining this feature, we can modify the Keiper--Li
scheme to obtain a new sequence in elementary closed form. This makes for a
more explicit analysis, with easier and faster computations. We can moreover
show how the new sequence will signal RH-violating zeros if any, by observing
its analogs for the Davenport--Heilbronn counterexamples to RH.
