The thing is with just labelling as 'recorded by' is that all of these list have songs which are listed on BMI and credits them as songwriters, but no one knows if they were ever recorded. I think different stylisations apply to different singles. Alexandra Burke and Cheryl Cole have hardly written any of their own material, so I think that they should be 'recorded', but for others like Katy Perry, Nicki Minaj, Adele, Alicia Keys, Emeli Sande, Mariah Carey etc they write all their material. So I think written by applies, but so does recorded by. Keys and Carey produce all their material too.  