Sometimes a Japanese person will say to me:

そんなに丁寧な言葉を使わなくてもいいんですよ。

This is an invitation to be less formal. But how much less formal? As I have experienced, sometimes unintentional gaffes can be committed blithely as one learns to navigate the treacherous waters of the politeness hierarchy. Note that the expression itself uses です even though it is a request to use less formal speech, and that is the level of politeness I would normally be using. So I find the whole matter confusing. The eternal politeness dance ...

Now, here's the catch: I feel it would be rude to ask something like "What level of politeness do you suggest I use?" That might come off as sarcastic or, worse, a rebuke. Any advice?