And, although Simon Grix responded, that was one of four Warrington tries which crucially went unconverted.
Five minutes later Glasgow confirmed their early superiority with a slick, though unconverted, try.
And there was further hope when Steve Winn crossed over in the 70th minute for an unconverted try.
Mark Dalle Cort's unconverted try made it 16-6 but Wigan were level through Cameron Phelps and Amos Roberts.
That left the Ospreys needing an unconverted try to pinch it and they hammered away at the Ulster line.
Biggar's excellent conversion tied the scores, but Ulster crept ahead again after Cave shook off Marty Holah for an unconverted score.
Yet they took the lead for the first time on 46 minutes as Kefu's break sent Lemi in for an unconverted try.
It is a culture he has spent his career trying to change and he will continue to preach his gospel to the unconverted.
Then Phillips' quick thinking, taking another tap, allowed Nick Robinson to send Morgan over untouched in the left corner for an unconverted try.
But Bradford reclaimed the lead three minutes before the break when scrum-half Matt Orford created the space to send Sykes over for another unconverted try.
Ulster went on the attack from the start and were rewarded when Best finished off great forward play with an unconverted try after five minutes.
BBC: SPORT | Rugby Union | European Club | Ulster 8-24 Biarritz
Kellock had just returned when Glasgow scored their second unconverted try.
Rob Miller and Mark Easter scored unconverted tries for the visitors in the final 10 minutes to ensure Sale did at least get on the scoreboard.
Carter fielded an aimless clearance and popped a simple ball to Muliaina on the scissors, allowing the full-back to race through almost untouched for an unconverted try.
And it was not long before they claimed their first try thanks to Tovey's cross-field kick which saw Harries go over in the corner for an unconverted try.
Scarlets put the ball through the hands and gave Gavin Evans enough space to cut inside Fa'atau and score an unconverted try, despite the efforts of Graeme Morrison.
The prospects for the residual 90 unconverted stores are unclear.
Wakefield hit back soon after through an unconverted try from Blanch in the right corner but a delicate offload from prop Joe Vagana ushered Harris over from 10 metres.
Nagusa did excellently to free his arms as he was tackled, finding Ian Whitten who off-loaded to Danielli for the wing's second try, although this time it went unconverted.
But the Dragons had the final say when they worked the ball wide for Blanch to go over for an unconverted first try of the season in the corner.
James did well to scoop up the ball as the pass fell just short and the prop earned his reward with a second try, although this one went unconverted.
The Scarlets stretched their lead after the break when Williams found a huge hole in the Blues midfield to scamper through and send lock Day over for an unconverted try.
Quick hands, swift pace and good running lines gave Lifeimi Mafi just enough space to squeeze in at the right corner flag, despite Lee Byrne's despairing tackle, for an unconverted try.
Portugal, who are at the start of their long process for 2011 World Cup qualification, were blitzed at the start going behind to three quick-fire unconverted tries by centre Cave, Nagusa and McCrea.
It looked as though Bath were going to head home pointless but Faamatuainu crashed through Russell's tackle for an unconverted try two minutes from time to hand the visitors a losing bonus point.
The Tigers then splintered the Treviso pack at an attacking five-metre scrum as the home forwards went back as though they were on rails and Crane dotted down out wide for an unconverted try.
Seoul's repatriation of "unconverted" political prisoners to the North was the latest development in the ongoing cross-border dEtente that started with the historic summit in June and continued with the limited family-reunion program last month.
Francis Maloney had given the Wildcats a lifeline with an unconverted try on 72 minutes that cut the gap to 24-22 after the Wolves had gone ahead with second-half tries by Nutley, Langer and McCurrie.
Italy once again lost control of the ball at the base after Bergamasco had been sucked into a ruck and Haskell's flick saw Ellis scamper 20m to the line and dive over for an unconverted try.
Laulala fed Rush and then followed the back-row on the inside shoulder, picking a pass off his shins for a deserved try that went unconverted - although Parks' kick was genuinely tricky close to the right touchline.
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