You can anonymously sign up to exchanges such as
- BTC-E
- LitecoinLocal
- Kraken
- Litetree
- VaultofSatoshi
- Bitfinex
- Crypto-Trade
- Bit2C
- BitBargain
- Vircurex
- Cryptsy
- X-BT
- Bter
- Coins-E
Deposit coin to one of them, then withdraw to another, and do this through a couple of exchanges.
Try use exchanges which have low withdrawal fees, if someone started to trace deposits and withdrawals through exchanges,
The more exchanges you tumble through, less likely they would be successful with tracing through every exchange.
Try not to purchase alt coins when tumbling, i don't think its necessary as 0.2% fee is charged on each trade. Also watch out for BTC-E as they put a 24-48 hour hold on coins which are deposited to newly created accounts.
They don't have to trace you through the exchanges.
It's called a subpoena.
All you're doing is creating an incredibly easy to follow paper trail through the exchanges. LE literally has to expend no effort at all to track it. Just get the transaction record for the input account and follow the output account to the next stop. Rinse. Repeat.
Ask Mt. GOX how not cooperating with LE worked out for them.