I think the best way to stay anonymous is to sell your bitcoins for whatever altcoin, then transfer those altcoins to another exchange and buy back your bitcoins. if the exchange is on Tor there is a good chance that the LEs will never get the data that could lead to your identity.
i ever try this method, and it's pretty cool really work, ok the explanation like this
i have some bitcoin then i bought dogecoin on other exchanger like bittrex,poloniex or yobit then i transfer to another wallet and then deposite to my local exchanger then sell it for bitcoin, tadaaaa they can't trace me
dogecoin has a low tx fee btw
Those other exchanges you use can trace you if they collude.
This is the same as just withdrawing and depositing to bitcoin casinos or other high-volume websites. The exchanging to altcoin only adds trading fees.
