I don't put coins through an online tumbler/mixer. Have never used one of those sites, so I don't have any reason to distrust them. But it seems like adding an unnecessary point of possible failure to the process.
I use Mycelium Android HD wallet. Let's say I buy 1 bitcoin from circle.com and move it to my current Mycelium public address. As soon as that transaction happens, Mycelium archives that address to a pool of legacy addresses and creates a new public address at the top-level. The new address has no history on the blockchain.
So now I send that coin to merchant XYZ with the sending addr being the new one. And circle.com, nor anybody else, has any way to connect the dots and follow the trail.
Am I correct that any time I add money to my wallet, and it creates a new address to send that money from, that bitcoin has been anonymized?
So from what I understand you're moving Circle --> Your Mycelium wallet --> Market? If it ever came down to it you could say you just sent it to a friend and thus you weren't responsible for that transaction. Kind of a flimsy argument though. And yes if circle wanted to they could connect the dots with your transaction, every transaction is recorded on the ledger.
If you don't want to tumble, you could be a little bit more secure by sending pieces of your circle bitcoins to separate electrum addresses. Then send those coins to a Mycelium wallet, then to a vendor. Or keep bouncing them around with fresh installs of both depending on how much you want to distance yourself from your coins.
Btw I'm no Bitcoin expert. If someone out there knows more and can correct me feel free.
To be honest though, unless you are a huge drug pusher, it's much more likely real life security will fuck you over, rather than digital security. That's not to say don't half ass your digital security, but it's not very likely LE will perform forensics on the blockchain to prove you ordered an O of weed