How many times can one come across a Velvet Underground song and describe it as one of the all-time classic rock & roll songs? As many times as Lou Reed wrote one that deserves such an appellation, of course, and even his detractors will admit that "Sweet Jane" deserves every grandiose epithet that has ever been heaped upon its head. Like "Waiting for the Man" and "White Light/White Heat," its partners in the upper echelons of glory, "Sweet Jane" is little more than a memorable riff, buoyed by a lyric that is almost outspoken in its openness — all the ingredients of a classic rock monster. And Reed knew that from the outset — the group's fourth (and final) album, from whence "Sweet Jane" comes, was titled Loaded because it was. Loaded with hits, that is. Heard on the Live 1969 album, recorded the night the song debuted in the Velvet Underground's live set, "Sweet Jane" is already a jewel. Yet the version that emerged on the original Loaded album release was only part of the picture. Post-production, pre-release, and completely unbeknownst to Reed, an entire section was sliced out of the song, a dramatic surgery that may have tightened the song for radio play, but utterly eviscerated the song. CD repackages have restored the absent section but the damage was already done — of the multitude of covers that "Sweet Jane" has provoked over the years, few ( Lou Reed included!) render the song in its full glory; fewer still ( Reed presumably not included) were even aware that such a beast even existed. And that, perhaps, is the greatest testament of all. Even hacked in half, "Sweet Jane" was still more of a song than most folks could even dream of writing.
(Dave Thompson, allmusic.com)