I think this is an improvement over the last. However, I really don't like the automatic importing of so many functions, particularly enter, leave and caught. I really think those should be optional. Consider the potential confusion of using this module next to Exception::Class which might be using it's own caught method! There's no real reason why you can't support variations like this:

use Log::Painless qw( :ALL ) { %opts };

use Log::Painless qw( :STD ) { %opts };

use Log::Painless qw( :NONE ) { %opts };

use Log::Painless qw( debug info ) { %opts };
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It's fine to have your own import, but it would be great -- even if you automatically import a few functions -- to allow users to turn that off if they want.

Also, while a minor point, I'd rather see the Pod follow a more standard format, with the abstract describing the module, not the document, with the synopsis being just a short amount of code, and what you wrote in the synopsis being retitled to "Description" or "Usage".