  We study the trap depth requirement for the realization of an optical clock
using atoms confined in a lattice. We show that site-to-site tunnelling leads
to a residual sensitivity to the atom dynamics hence requiring large depths (50
to $100 E\_r$ for Sr) to avoid any frequency shift or line broadening of the
atomic transition at the $10^{-17}-10^{-18}$ level. Such large depths and the
corresponding laser power may, however, lead to difficulties (e.g. higher order
light shifts, two-photon ionization, technical difficulties) and therefore one
would like to operate the clock in much shallower traps. To circumvent this
problem we propose the use of an accelerated lattice. Acceleration lifts the
degeneracy between adjacents potential wells which strongly inhibits
tunnelling. We show that using the Earth's gravity, much shallower traps (down
to $5 E\_r$ for Sr) can be used for the same accuracy goal.
