It depends on the client you're using and the method you're using to communicate. Confusing... I know. If you're using Snort, Amethyst, Nostrudel, Coracle to 0xChat then your DMs and their metadata are private. If you're using Primal, Damus and others, then the DMs are private but the metadata is leaked. There's a new standard being worked on now by nostr:nprofile1qqspwwwexlwgcrrnwz4zwkze8rq3ncjug8mvgsd96dxx6wzs8ccndmcpzdmhxue69uhhqatjwpkx2urpvuhx2ue0qyd8wumn8ghj7urewfsk66ty9enxjct5dfskvtnrdakj7qghwaehxw309aex2mrp0yhxummnw3ezucnpdejz7l352lu and the hope is that everyone upgrades to it when he's done. 

 Thanks Derek!
Is the work of  @JeffG somehow related with disposable nsecs? 

 no. this work that im talking about here is about using MLS (a messaging protocol) with nostr, to give us better and more private DMs. 

 Cool. I'll keep an eye on it.  Thanks. 

 Parts of the spec use disposable keys (for gift wrapping) but like Derek said, the real benefits come from using MLS. You can read more if you look up NIP-104 on the NIPS repo. Happy to answer questions though.  

 Thank you Jeff for the answer.  Would you please point me to the correct repo?  I'm not sure if I'm searching in the right place :P