  Linear axion monodromy models modulated with higher powers of fields
naturally realize the quantum-mechanical flux discharge mechanism for relaxing
the cosmological constant toward zero. Working with multiple copies of
superposed linear and quadratic flux monodromies, each copy spanned by a pair
of fluxes, we show that when the axion is very massive and so effectively
decoupled, the membrane discharges relax the cosmological constant toward an
attractor $0 < \Lambda/\mpl^4 \ll 1$. If we restrict the flux variations and
the intermediate flux values to never venture beyond a finite flux range, the
terminal value of the cosmological constant will be tiny but finite. We show
how it can reproduce the observed scale of dark energy, and explain how to
incorporate matter sector phase transitions.
