A new fitting methodology is presented which is equally well suited for the estimation of low-, medium-, and high-degree mode parameters from $m$-averaged solar oscillation power spectra of widely differing spectral resolution. This method, which we call the Windowed, MuLTiple-Peak, averaged spectrum, or WMLTP Method, constructs a theoretical profile by convolving the weighted sum of the profiles of the modes appearing in the fitting box with the power spectrum of the window function of the observing run using weights from a leakage matrix that takes into account both observational and physical effects, such as the distortion of modes by solar latitudinal differential rotation. We demonstrate that the WMLTP Method makes substantial improvements in the inferences of the properties of the solar oscillations in comparison with a previous method that employed a single profile to represent each spectral peak. We also present an inversion for the internal solar structure which is based upon 6,366 modes that we have computed using the WMLTP method on the 66-day long 2010 SOHO/MDI Dynamics Run. To improve both the numerical stability and reliability of the inversion we developed a new procedure for the identification and correction of outliers in a frequency data set. We present evidence for a pronounced departure of the sound speed in the outer half of the solar convection zone and in the subsurface shear layer from the radial sound speed profile contained in Model~S of Christensen-Dalsgaard and his collaborators that existed in the rising phase of Solar Cycle~24 during mid-2010.
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