It has been known for 35 years that phase correction of FTICR data can in principle produce an absorption-mode spectrum with mass resolving power as much as a factor of 2 higher than conventional magnitude-mode display, an improvement otherwise requiring a (much more expensive) increase in magnetic field strength. However, temporally dispersed excitation followed by time-delayed detection results in steep quadratic variation of signal phase with frequency. Here, we present a robust, rapid, automated method to enable accurate broadband phase correction for all peaks in the mass spectrum. Low-pass digital filtering effectively eliminates the accompanying baseline roll. Experimental FTICR absorption-mode mass spectra exhibit at least 40% higher resolving power (and thus an increased number of resolved peaks) as well as higher mass accuracy relative to magnitude mode spectra, for more complete and more reliable elemental composition assignments for mixtures as complex as petroleum.