I use one of these neoprene carry bags:
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1
It is slightly too large for just a PaperWhite (they make smaller sizes too), but I have my larger Fire HD8 in there with the PaperWhite. It's a snug fit that relaxes over time. Perfect for what I wanted (some kind of handle to carry the thing, so I won't fumble and drop it).
The Fire has this case attached to it:
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1
Then the PaperWhite has no individual case, but is put in the carry bag with it's screen facing the Fire, so it's well protected.
I like the small size and low weight of the PaperWhite. Adding an individual case to it somewhat defeats those two good attributes. So the carry bag is ideal for what I wanted.
In the side pocket of my little carry bag, I also have an super small MP3 player, some earbuds, some in-the-ear hearing protectors (so I can block out noise if I'm reading the Kindle), and a stylus for detailed work on the Fire. And for this last week, I also put my Nook Simple Touch in the main compartment. So I had a sandwich - Nook on one side, PaperWhite on the other, Fire in the middle. Initially this much stuff would have been a tight squeeze. But it all fits fine now, after 6 months use worth of stretch on the neoprene. This case appears to have been custom made for the Fire HD8. It fits perfectly. And I do mean perfectly!
Mine is black, but the link above doesn't show that color currently. But these little neoprene bags are all over Amazon. Five million different vendors for them, with varying manufacturer names and varying prices (all are cheap though). They are probably all identical, coming out of the same factory in China or Guatemala.
It's my little "entertainment bag". (Don't call it a purse, because guys used to get beat up for carrying purses!)