NMR spectra acquired with experiments using frequency-sweeps such as the wide-band uniform-rate smooth truncation (WURST) spin-echo and Carr-Purcell-Meiboom-Gill (CPMG) sequences cannot be absorptively phased by using only conventional zeroth- and first-order phase correction. Implementation of phase correction up to the second-order is described for obtaining absorptive spectra, which have more desirable line shapes and noise properties than magnitude spectra. The relationship of the second-order phase to the parameters of frequency sweeps is derived. The second-order phasing in the frequency-domain is equivalent to a point spread in the time-domain signal. The application of second-order phase correction is demonstrated with a wideline 35Cl CPMG spikelet spectrum.