Gaylord Fields played Witchi-Tai-To by Everything Is Everything, a jazz/funk/rock group sax player Jim Pepper formed in 1969 with guitarist Chris Hills. The track became well known the same year, covered by Brewer And Shipley, and played by Dan Bodah on Airborne Event, but was also revisited in 1970 by Pepper on Pepper's Pow Wow, chosen by John Allen.
WFMU often plays obscure cover versions of well known songs. Duane played "Light My Fire" and "God Only Knows" by Erma Thomas And Betty Evertt respectively. You are drawn in and grounded by the familiarity of the track, but hearing the familiar with a different treatment makes you listen for the changed details of the song, and you're more attuned to the next record the DJ plays. Hear how Bennentt4Senate, on Awesome New Place, uses Stardive's cover of "Strawberry Fields Forever" to segue into "Somewhere Out There" by Meow's Affectionate Century.
In the 1960's, an artist who didn't write his or her own material would cover huge hits. "You've Made Me So Very Happy" is from 1969, when Blood Sweat And Tears ruled the charts, providing an artistically viable but mainstream-safe alternative to counter culture rock. Hatch played Lou Rawls performing the track, while Meghan played an Alton Ellis' cover on Underwater Theme Park in a show about "being happy". I think these are good covers: you may disagree. But more interesting is imagining DJ's with freedom shopping in fifty cent bins, finding a record that is never played on commercial radio--and was counterpoint to progressive FM hipness when issued---and thinking "hummm....how can I make this sound good?" Thrift shop debris becomes an essential part of free-form radio gestalt.