@dgarretson, I realize mine is a minority opinion, but yes, it was in the Summer of '68 I saw/heard them live. The guys in Big Brother exemplified everything that was wrong with hippie musicians, and Janis was doing her standard "shrieking/screeching" style of white-girl Blues "singing". You know, trying too hard to be "soulful". Cheap Thrills was produced by John Simon; John also produced the first two superlative Band albums, so the blame can't be laid at his feet. Hey, you can't make a silk purse out of a sow's ear. ;-)
For anyone who wants to hear how it CAN be done, give a listen to Lou Ann Barton. She has a few solo albums, and often tours with Jimmie Vaughan. She was the singer in the original version of Double Trouble, when Stevie Ray was "only" playing guitar in the band. Her fantastic Old Enough album was produced by Glenn Frey and Jerry Wexler, Wexler Aretha's producer at Columbia Records. Now THERE'S a great white woman Blues singer.