In Barcelona, the former champions took a clear step closer to runaway pacesetters Mercedes and Ferrari.
“We closed more than 60 per cent of the gap,” Red Bull official Dr Helmut Marko told Salzburger Nachrichten newspaper.
He admitted the team is hoping for another big step in time for the Red Bull-promoted Austrian grand prix in July.
But that also depends on whether the Renault upgrade will be ready by then.
“Naturally we are hoping that something will come before Austria,” he said.