Rescuers are within one metre (3ft) of two miners trapped underground in a Tasmania mine, and have successfully driven a probe drill into the cavity.
Australians have been gripped by the story of the rescue
The probe suggested there was as little as 30-40cm of hard rock left to cut, as the remaining 60cm is loose rock.
But the rescuers are approaching the cavity from underneath, and are taking precautions to avoid further rock falls, so progress is slow.
Todd Russell and Brant Webb have spent nearly two weeks in a steel cage.
The cage saved the lives of the two men when the Beaconsfield Gold Mine in Tasmania was hit by a small earthquake on 25 April.
Union official Bill Shorten has cautioned that the miners might not be freed before Tuesday morning.
But he welcomed the news that the final stretch of rock separating rescuers from the men was "not as thick as expected.
"For once we've had a break our way - it's some long overdue good news," he told Associated Press.
Mr Russell, 34, and Mr Webb, 37, survived for five days on just one shared cereal bar and by licking water from the rocks around them, before rescuers discovered they were alive by using a thermal imaging camera.
The funeral of Larry Knight, 44, a fellow miner who died in the rockfall, is to go ahead on Tuesday after his family said they could wait no longer for the release of the two survivors.
Rescuers have worked painstakingly for days to cut through rock described as five times as hard as concrete to reach the men.
THE TRAPPED MINERS
Todd Russell: 34, married with three children
Wants paramedics to stop off at fast-food joint after rescue
Asked for newspaper to scan for other jobs and overtime pay
Brant Webb: 37, married to childhood sweetheart
Also has three children, including teenage twins
Both men have requested they walk out of the rescue tunnel
They now have to turn upwards to approach the cavity from below.
Reports suggest the rescuers will zig-zag towards the cavity to avoid further rockfalls.
The trapped men are also said to be helping the rescue effort by using grout to secure loose rocks at the base of the cavity.
Rescuers are also constructing a vertical escape shaft to prevent a cave-in when the men are finally reached.
"If you dislodge this fill in the wrong way all of a sudden a whole lot of other dirt can fall into this tunnel and you could dislodge the rocks which led to the fatality of Larry Knight," Mr Shorten said.
A narrow PVC pipe connects the men to paramedics, through which they have been passed food and drinks. They have also been given iPods to help pass the time, an inflatable mattress, a digital camera and a light exercise programme to ward off health problems.
The men's plight and the sense of humour they have displayed to emergency workers has gripped Australia, leading to reports of a media scramble to secure exclusive rights to their story when they do emerge.
A shadow was cast over the rescue efforts on Sunday, when a prominent TV reporter covering the story died at a news conference.
Richard Carleton - an award winning reporter with the Nine Network's 60 Minutes programme - had asked a question of the mine manager only moments before he collapsed of a suspected heart attack.