The Spurs pair are in Oslo for Norway's opening World Cup qualifying match against Armenia at the Ullevaal Stadium.
They are first to admit that Norway have disappointed in major finals so far. It was the same story this summer when they were knocked out at the group stage of the European Championship after only scoring one goal - Iversen's header against Spain in the first game.
Now they face a tricky qualifying campaign starting against Armenia with further matches against Sergei Rebrov's Ukraine, Poland, Wales and Belarus.
Striker Iversen admitted: "It's important for us to get a good start. We had a bad European Championship and then lost a friendly against Finland a couple of weeks ago. We have to get back on track.
"It would be a dream to play in the World Cup. I've played in the European Championships now and have that little bit of experience and if we can qualify for the World Cup we can show the people that we are better than how we played in the summer.
"We still don't perform in the big championships. I don't know why and there is no logic to it. We try to play the same football but it just doesn't happen for us. Hopefully we can qualify well and show everyone that we are a better team we have showed so far."
Leonhardsen agreed with Iversen's sentiments: "We've been a bit disappointed with the way we've played in the World Cups," said the midfielder. "Hopefully we can get there for a third time and play a lot better.
"We have been in two World Cups and one European Championship and not produced it in the finals. First we have to qualify, which will be hard, but we have done well in the last few qualifying campaigns. Perhaps it will be harder because the expectation levels are higher. Hopefully we can get there again and show the world we can play better football."
Steffen Iversen and Oyvind Leonhardsen are both determined to show the world what Norway can do.