We present an adaptation of the rotation-corrected, m-averaged spectrum technique designed to observe low signal-to-noise ratio (S/N), low-frequency solar p-modes. The frequency shift of each of the 2l + 1 m spectra of a given (n, l) multiplet is chosen that maximizes the likelihood of the m-averaged spectrum. A high S/N can result from combining individual low S/N, individual-m spectra, none of which would yield a strong enough peak to measure. We apply the technique to Global Oscillation Network Group and Michelson Doppler Imager data and show that it allows us to measure modes with lower frequencies than those obtained with classic peak-fitting analysis of the individual-m spectra. We measure their central frequencies, splittings, asymmetries, lifetimes, and amplitudes. The low frequency, low- and intermediate-angular degrees rendered accessible by this new method correspond to modes that are sensitive to the deep solar interior down to the core (l <= 3) and to the radiative interior (4 <= l <= 35). Moreover, the low-frequency modes have deeper upper turning points, and are thus less sensitive to the turbulence and magnetic fields of the outer layers, as well as uncertainties in the nature of the external boundary condition. As a result of their longer lifetimes (narrower linewidths) at the same S/N the determination of the frequencies of lower frequency modes is more accurate, and the resulting inversions should be more precise.