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We present a comprehensive study of one method for measuring variousparameters of global modes of oscillation of the Sun. Using velocity data takenby the Michelson Doppler Imager (MDI), we analyze spherical harmonic degrees l<= 300. Both current and historical methodologies are explained, and thevarious differences between the two are investigated to determine their effectson global-mode parameters and systematic errors in the analysis. Thesedifferences include a number of geometric corrections made during sphericalharmonic decomposition; updated routines for generating window functions,detrending timeseries, and filling gaps; and consideration of physical effectssuch as mode profile asymmetry, horizontal displacement at the solar surface,and distortion of eigenfunctions by differential rotation. We apply thesechanges one by one to three years of data, and then reanalyze the entire MDImission applying all of them, using both the original 72-day long timeseriesand 360-day long timeseries. We find significant changes in mode parameters,both as a result of the various changes to the processing, as well as betweenthe 72-day and 360-day analyses. We find reduced residuals of inversions forinternal rotation, but seeming artifacts remain, such as the peak in therotation rate near the surface at high latitudes. An annual periodicity in thef-mode frequencies is also investigated.

Improved Helioseismic Analysis of Medium-l Data from the Michelson Doppler Imager