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Australian banks, just like most other banks, need history with transactions to prove you have established banking credibility. National bank of Australia credits my account on any cheque I deposit instantly, no matter how big the cheque.
At the start, I had to wait the 2-6 weeks for internationally drawn cheques too. Just speak to whoever you're with, tell them you want to get your cheques cleared sooner, if you have some history with them.
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