They currently sit seventh in the table after gaining a losing bonus point against Connacht before following that up with a 13-0 win over Zebre last time out.
But Tovey insists there is still more to come from the Dragons, including being more clinical when it comes to putting points on the board.
The Welsh outfit do, however, travel to the RDS buoyed by completing a first ever season's double over the Leinstermen last year, with a 16-14 victory in the Irish capital last February their first success in 12 attempts.
And Tovey is determined to try and build on that run when they lock horns again this weekend.
"That win means we go there with confidence and sometimes we play better away from home," Tovey told the South Wales Argus.
"It's up to the home team to entertain and we put pressure on them.
"As long as we do that again then there's no reason why we can't win there again. They won't be taking us lightly after last season but we just have to concentrate on getting our game right.
"And after both our games (against Connacht and Zebre this season) we have spoken about the need to be more clinical.
"If we weren't creating chances we'd be more worried but better teams will punish us if we aren't putting points on the board."
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Guinness PRO12 Dragons News
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