The RCR Wireless article no longer appears online but Mr Lawrey's quotes remain on the Australian technology news website iTnews, which repeated them.
RCR Wireless quoted Mr Lawrey as saying Telstra would also take action against customers believed to be abusing the carrier's fair-use policies.
"We probably haven't even used our fair use small print yet. But we will," Mr Lawrey reportedly said.
He was also reported to have said that if the carrier's proposed system "cut out 80 per cent of the non-value adding traffic – good".
According to the RCR Wireless article, about 80 per cent of Telstra's data was chewed up by high bandwidth users.
"I'd rather not have those 80 per cent as customers. I'd rather someone else had them as customers," Mr Lawrey reportedly said. He did not say whether he was talking about fixed-line, smartphone customers or both.
Exetel, a smaller ISP than Telstra, used to throttle, or "deprioritise", peer-to-peer traffic during peak periods. Its terms and conditions say it can still do so but a staff member last year said on its forum that it did not shape "any type of traffic".
Illegal downloading via BitTorrent networks has been in slight decline for some time, though reports suggest there was a small rise in 2012. In part that would be fuelled by faster internet services worldwide and a migration away from traditional television in which some consumers now exclusively watch TV content via the internet.
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