  The sequestering mechanism has been proposed as a remedy to the old
cosmological constant problem of the non-gravitating vacuum energy in the
matter sector. Here it is shown that an extension of this global constraint
mechanism arises naturally from an averaging condition for residual
cosmological constants produced in different patches of the Universe. The new
mechanism naturally yields the small observed value that gives rise to cosmic
acceleration at late times, hence, addressing the new cosmological constant
problem. Hereby the halo model picture is adopted with all matter content
ultimately residing in the last collapsed structures formed. Sequestering in
these collapsing patches produces the desired average residual, where a uniform
prior on our present location in the collapse predicts
$\Omega_{\Lambda}=0.697$. Finally, a fluctuation of the local residual from the
cosmological average can naturally give rise to a locally enhanced Hubble
constant.
