The Men from the North are still in there, hanging on by their fingertips.
The bonus-point win over the Scarlets in Belfast was mandatory to their unrealistic ambition to qualify for the Champions Cup quarter-finals.
Was it merely a stay of execution? Was it it the opening shot in a miracle resurgence?
The hole Leicester Tigers put in Toulon made the holders look vulnerable, very vulnerable at times.
Ulster will probably rue the day they didn't turn up against them in round two.
At least, they can maintain their interest by taking another five points from Scarlets. It is the least they will need to steel themselves.
BAYONNE v CONNACHT, Tomorrow, Stade Jean Dauger (KO 7.45)
Connacht have played this French club three times in Europe and three times they have won.
The most recent, last Saturday, was good enough to place the Westerners on 10 points, right on the coat-tails of Pool Two leaders Exeter Chiefs, on 11.
The interest of Bayonne will be central to how this will go. If they want it, Connacht will have to be razor-sharp. If they don't, the Irish province won't.
"We know it will be a different story in Bayonne," said coach Pat Lam.
"That's the next task and we won't be getting carried away.
"We will have to be ruthless or teams like Bayonne are capable of punishing you."