Back in May, Jefferies masterminded his first win over an Old Firm side since taking charge at Kilmarnock when his players inflicted the first domestic defeat of Smith's second spell as Rangers boss.
Kilmarnock's goalscorer on that occasion, Steven Naismith, has since swapped sides and now lines up for Rangers.
But Jefferies insists his side should do themselves justice against either Rangers or Celtic these days - providing they show the right attitude.
He said: "We're contesting better. A few years ago we were getting battered by four or five goals, and I'm not saying that won't happen again.
"But we have competed better against the Old Firm in the last two or three years, we've given them much tougher games and that's what I want to do this weekend.
"We played well that day but the difference was we had a match-winner in our side in Steven Naismith and now he's on the other side.
"We know what Steven's capable of, so we had better make sure we don't give him too many opportunities if he plays.
"We've got to make sure we do the right things as they have far better players than us, have a far better squad than us.
"If you do that you've got a better chance of getting a result, but you also need luck along the way at places like Ibrox or Parkhead as it's hard to contain them for 90 minutes.
"You need to concentrate hard, keep your discipline and most of all belief.
"If we need any improvement on belief surely we can get it from the last time we went there because we managed to get a win and that does wonders for your confidence."