The axial resolution of fluorescence microscopes can be considerably improved by superposing two illumination beams and by adding coherently the two wavefronts emitted by the luminescent sample. This solution has been implemented in 4Pi microscopes. Theoretical and experimental results have shown that a considerable improvement of the axial resolution can be obtained with these microscopes. However, the lateral resolution remains limited by diffraction. We propose a configuration of a 4Pi microscope in which the lateral displacement of the source modify the Collection Efficiency Function (CEF). Numerical calculations based on an approximated scalar theory and on exact vector-wave-optics results of the field distribution of the electromagnetic field in image space, show that the lateral extent of the CEF can be reduced by a factor greater than two with respect to the diffraction limit. We show that, with this solution, the resolution in the transverse plane of 4Pi type B and 4Pi type C microscopes can be improved significantly.