Recently, C. Imbert & R. Monneau study the homogenization of coercive
Hamilton-Jacobi Equations with a u/e-dependence : this unusual dependence
leads to a non-standard cell problem and, in order to solve it, they introduce
new ideas to obtain the estimates on the oscillations of the solutions. In this
article, we use their ideas to provide new homogenization results for
``standard'' Hamilton-Jacobi Equations (i.e. without a u/e-dependence) but in
the case of {\it non-coercive Hamiltonians}. As a by-product, we obtain a
simpler and more natural proof of the results of C. Imbert & R. Monneau, but
under slightly more restrictive assumptions on the Hamiltonians
