Delivering femtosecond laser light in the focal plane of a high numerical aperture microscope objective is still a challenge, despite significant developments in the generation of ultrashort pulses. One of the most popular techniques, used to correct phase distortions resulting from propagation through transparent media, is the multiphoton intrapulse interference phase scan (MIIPS). The accuracy of MIIPS, however, is limited when higher-order phase distortions are present. Here we introduce an improvement, called G-MIIPS, which avoids the shortcomings of MIIPS, reduces the influence of higher-order phase terms, and can be used to more efficiently compress broadband laser pulses even with a simple 4f pulse shaper setup. In this work, we present analytical formulas for MIIPS and G-MIIPS, which are valid for chirped Gaussian pulses; we show an approximated analytic expression for G-MIIPS, which is valid for arbitrary pulse shapes. Finally we demonstrate the increased accuracy of G-MIIPS via experiments and numerical simulations. (C) 2014 Optical Society of America