The article studies a second-order linear differential operator of the type - L = X 1 2 + ⋯ + X r 2 , i. e., a sum of squares of real, and real-analytic, vector fields X i . The conjectured necessary and sufficient condition for analytic hypo- ellipticity, based on the Poisson stratification of the characteristic variety, is recalled in simple analytic and geometric terms. It is conjectured that the microlocal Gevrey hypo-ellipticity of L depends on the restrictions of the principal symbol σ L to 2 D or 4 D symplectic manifolds associated to each bicharateristic curve in a nonsymplectic stratum.