An interior penalty method and a compact discontinuous Galerkin method are proposed and comparedfor the solution of the steady incompressible Navier–Stokes equations. Both compact formulations canbe easily applied using high-order piecewise divergence-free approximations, leading to two uncoupledproblems: one associated with velocity and hybrid pressure, and the other one only concerned with thecomputation of pressures in the elements interior. Numerical examples compare the efficiency and theaccuracy of both proposed methods.