The record-breaking band rocketed to fame after being plucked from obscurity on ITV's Popstars programme.
After a chart-topping album and two No1 singles the band booked 36 UK dates and opened the tour in Cardiff on August 25.
But hundreds of tickets are still available with only four of the band's remaining 20 concerts sold out.
A Hear'Say spokesman was adamant that lack of ticket sales didn't mean the group's bubble had burst.
He said: "It is a very big tour with 36 dates at some of the country's biggest venues.
"So far we have sold 85% of the tickets and we are very confident that we will sell the remaining tickets."
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