You might consider this a follow-up from a couple of sources. First, "Sid to Hakuchumu" (Sid and the Daydream) was a track on Ringo Shiina's（椎名林檎） great 1st album, "Muzai Moratorium"（無罪モラトリウム）. Unfortunately, I didn't include the song into that article, so I'm making one up right here for it. And then I did mention it in the article for her 7th single, "Mayonaka no Junketsu"（真夜中の純潔）since a Big Band version existed as one of the extra songs on the CD.
The original version was written and composed by Shiina when she was 19 years old (so around 1997) but didn't get officially recorded until her debut album in 1999. I heard bits and pieces of "Sid to Hakuchumu" throughout the various music shows as "Muzai Moratorium" went up the charts, and listening to this song along with some of the other tracks, I just thought that this singer was definitely one interesting and scary lady. The shrieking vocals with that yakuza/Scottish burr didn't hurt either. Going back to "Sid to Hakuchumu", though, even listening to the version above, I could hear a bit of that jazziness through the bass beyond all that buzzy guitar and synth.
But I have to admit that I really became a fan of the song when I bought "Mayonaka no Junketsu" in 2001 and came upon the Big Band self-cover of "Sid". Arranged by composer/conductor Takayuki Hattori（服部隆之）, I just felt like Shiina got transported from the century's-end alleyways of Kabukicho to the studio stage of the Nat King Cole show in America in the 1950s. I don't know if there was ever an official video for this version but if there were, I could see the singer belting away in front of a tuxedoed big band with the stylized initials of "R.S." emblazoned in gold on each of the musicians' front stands. Legendary bandleaders Nelson Riddle and Lawrence Welk would have been green with envy. "Wunnerful, wunnerful" as Welk would have said.