  Recently two of the authors proposed a mechanism of vacuum energy sequester
as a means of protecting the observable cosmological constant from quantum
radiative corrections. The original proposal was based on using global Lagrange
multipliers, but later a local formulation was provided. Subsequently other
interesting claims of a different non-local approach to the cosmological
constant problem were made, based again on global Lagrange multipliers. We
examine some of these proposals and find their mutual relationship. We explain
that the proposals which do not treat the cosmological constant counterterm as
a dynamical variable require fine tunings to have acceptable solutions.
Furthermore, the counterterm often needs to be retuned at every order in the
loop expansion to cancel the radiative corrections to the cosmological
constant, just like in standard GR. These observations are an important
reminder of just how the proposal of vacuum energy sequester avoids such
problems.
