Complex sentence: When Jagger's song failed to crack the Top 40, Yankovic considered not recording his version; because Jagger had "authorized" the parody, however, he decided failing to produce it would be an insult to the artist and recorded it.
Split into simpler sentences: When Jagger's song failed to crack the Top 40, Yankovic considered not recording his version. Because Jagger had "authorized" the parody, however, he decided failing to produce it would be an insult to the artist and recorded it.