AAPT is considering extending the six-hour window for unlimited off-peak downloads on a range of ADSL2+ plans launched in late May.
The move is understood to be one of several under consideration after a first six weeks that the ISP said had "exceeded expectations".
AAPT reported a 15 percent surge in the number of contracted broadband customers between May and June - an increase the service provider attributed to the unlimited plans.
"Demand for the unlimited offer has been so positive that we're planning to expand the features of the offer in the coming months, [including] bundles, content opportunities [and] possibly extending off-peak hours," a spokeswoman for the telco said.
She declined to produce download statistics but told iTnews that customers clearly understood "how to use download schedulers".
There was a "noticeable" drop in download traffic at 8am AEST, when the period for unlimited download (which starts at 2am) ends.
The unlimited off-peak offer had also benefited AAPT by enabling easier capacity planning on the network.
"The total volume of customer downloads are now more even across the entire 24 hour period, with larger files being downloaded in the off-peak period," the spokeswoman said.
"This has reduced the peaks and troughs in customer usage allowing for easier management of our network requirements."