  We present a new and highly efficient algorithm for computing a power
spectrum made from evenly spaced data which combines the noise-reducing
advantages of the weighted fit with the computational advantages of the Fast
Fourier Transform (FFT). We apply this method to a 10-year data set of the
solar p-mode oscillations obtained by the Birmingham Solar Oscillations Network
(BiSON) and thereby uncover three new low-frequency modes. These are the l=2,
n=5 and n=7 modes and the l=3, n=7 mode. In the case of the l=2, n=5 modes,
this is believed to be the first such identification of this mode in the
literature. The statistical weights needed for the method are derived from a
combination of the real data and a sophisticated simulation of the instrument
performance. Variations in the weights are due mainly to the differences in the
noise characteristics of the various BiSON instruments, the change in those
characteristics over time and the changing line-of-sight velocity between the
stations and the Sun. It should be noted that a weighted data set will have a
more time-dependent signal than an unweighted set and that, consequently, its
frequency spectrum will be more susceptible to aliasing.
