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In Part I we have developed a theory for fitting p-mode Fourier spectraassuming that these spectra have a multi-normal distribution. We showed, usingMonte-Carlo simulations, how one can obtain p-mode parameters using 'MaximumLikelihood Estimators'. In this article, hereafter Part II, we show how to usethe theory developed in Part I for fitting real data. We introduce 4 newdiagnostics in helioseismology: the $(m,\nu)$ echelle diagramme, the crossechelle diagramme, the inter echelle diagramme, and the ratio cross spectrum.These diagnostics are extremely powerful to visualize and understand thecovariance matrices of the Fourier spectra, and also to find bugs in the dataanalysis code. These diagrammes can also be used to derive quantitativeinformation on the mode leakage and noise covariance matrices. Numerousexamples using the LOI/SOHO and GONG data are given.Comment: 17 pages with tex and ps files, submitted to A&A,  thierrya@so.estec.esa.n

The art of fitting p-mode spectra. II. Leakage and noise covariance matrices