Jean-Eric Vergne and Daniil Kvyat completed 128 laps between them in Melbourne on Friday, more than any other driver pairing on the grid.
However, both suffered several off-track excursions as they struggled with the electronic system that compensates for the alteration in brake balance as kinetic energy is recovered from the rear axle.
The secrets of brake-by-wire
Vergne still went on to set a best laptime less than 1.5 seconds slower than Lewis Hamilton's pacesetting Mercedes in the second session, but the Frenchman believes the Toro Rossos will be much closer to the pace if they can get on top of their braking issues.
"Sometimes you've got this massive recharging at the rear, which recharges too much, so you have locking at the rear," Vergne explained.
"Sometimes it doesn't want to recharge and the brake goes all forward and you have no brakes on the rear and you lock the front and just go straight in the gravel.
"So it's quite good we don't start the season in Monaco!"
The Frenchman could not say whether improvements to the Renault engine had introduced new issues for the braking by wire system, which did not seem to adversely affect Toro Rosso in pre-season testing.
"To be honest I don't know," added Vergne. "But performance wise today was not too bad considering the problems I'm having on the braking right now.
"We can work on it. To have succeeded the day how we did with this problem was really good, and I believe if we can get over this problem we'll be in really good shape."
F1 rookie Kvyat said the braking issues were hurting his confidence as he tried to get to grips with the demands of the Albert Park street circuit for the first time.
"I'm not feeling too confident in that part of the driving to be honest," he said.
"On this track the last problem you want to have is on the brakes. It was hurting me being new, because my confidence is not really good.
"I had to really go under my limit in some corners because I just didn't know what to expect. But it all can be sorted out easily I think."
- Jean-Eric Vergne
- Toro Rossos
- Lewis Hamilton