Dynamical relaxation mechanisms for the cosmological constant (c.c.) commonly feature important drawbacks which rule them out as a solution to the c.c. problem. In this talk I will argue that the recent progress in understanding effective field theories that consistently violate the null energy condition (NEC) can breathe new life into non-anthropic approaches to the c.c. I will present a technically natural scenario, whereby an initially large cosmological constant is relaxed down to the observed value in a realistic universe.