Laser ponderomotive self-focusing in an underdense homogeneous plasma is studied within the paraxial complex geometrical optics (PCGO) approach implemented in a hydrodynamic code in two-dimensional planar geometry. The self-focusing of a PCGO Gaussian beam is compared to simulations performed with a paraxial electromagnetic code. Good agreement has been found for beam powers less than three times the critical power and for plasma densities 5%–10% of the critical density. Besides Gaussian beams, PCGO allows to reproduce spatially modulated beams by superposition of Gaussian beams, mimicking a speckle pattern. Although the statistics of speckle patterns generated with PCGO reproduces well the speckle statistics of optically smoothed beams, a PCGO speckle is larger than optical speckles, carrying thus higher power such that they overestimate self-focusing effects. To overcome this issue, an algorithm is proposed within PCGO framework: it consists of superposing several Gaussian beams forming a speckle such that self-focusing effects are eventually well controlled. It is found that the superposition of three Gaussian beams with appropriate initial conditions leads to a reduction of the PCGO speckle intensity enhancement.