He knows his side's strengths, particularly in an attacking sense, can also be their weakness against the Glasgow club, with the 1997-98 season being a perfect case in point.
Most Hearts fans only remember one game against Rangers that season and rightly so - a 2-1 victory in the Scottish Cup Final at Parkhead seeing the Tynecastle trophy cabinet filled with silverware for the first time in 42 years.
What has long since been forgotten is what happened in the four previous meetings between the two sides that season, Hearts only managing to take a single point off Walter Smith's side and, significantly, conceding 13 goals in the process.
To have a chance of turning the formbook on its head in the final, Jefferies and Billy Brown knew they had to change something about the way their side was set up, the work on a new 4-5-1 system being put in at the team's base in the early part of that week in Stratford-upon-Avon.
And, though a first-minute penalty in the east end of Glasgow definitely made their task a lot easier, Steve Fulton, who lifted the trophy as stand-in captain for the injured Gary Locke, reckons it was a day when the Hearts management duo showed they are far more tactically astute than some people give them credit for.
"The gaffer and Billy sometimes give the impression that they don't work too much on tactics compared to some other management teams, but it is a big part of their make up and always has been," said the man who first played for Jefferies at Falkirk, spent seven seasons at Tynecastle after becoming one of his first signings and then had another two seasons with him at Kilmarnock.
"A lot of the systems teams use a lot these days were the ones we played, a good example of that being that Stefano Salvatori was the sitting midfielder, giving myself and Colin Cameron a licence to go forward.
"When I was at Hearts, the gaffer and Billy built a team of players who complemented each other. They've not had the time to do that with the current team but they're having a positive effect on the players.
"You can see that with recent results in particular and I'm sure they will have the current team just as well organised for going to Ibrox on Saturday as we were for the 1998 Scottish Cup Final at Celtic Park.
"People forget that we had been well beaten by Rangers (3-1, 5-2 and 3-0) in most of the league games that season and, though we knew we had the players to finally get the better of them, we worked on a different gameplan at our training base down at Stratford.
"The main aim was to make it harder for Rangers to break us down and we all knew what roles we had to play that day. Of course, when we then scored in the first minute, it made our system that day even better.
"Every single one of us was focused on our specific job and, though we were a bit lucky at times in the game, I think we deserved that at the end of a season when we had also pushed Celtic and Rangers in the title race."
Hearts head for Ibrox on Saturday bidding to record their first win in Govan for than six years, Joe Hamill scoring the only goal of the game in a league victory in the penultimate game of the 2003/04 season.
Fulton, who works as a labourer these days but has retained his link with football as Falkirk Under-17s coach - his three sons play for the club at various levels - says it won't be easy for his old outfit, especially against a Rangers team that is marshalled so well by his big buddy David Weir.
But, with Marius Zaliukas doing the same job just as effectively for Hearts, Marian Kello in fine form and Kevin Kyle proving a handful at the moment, he certainly believes they should be making that journey this week feeling hopeful.
"I don't mean this to sound disparaging in any way but I think the calibre of the players at both Celtic and Rangers was a bit more special when we used to go through to Ibrox and Celtic Park," added the 40-year-old.
"It was often a case of battening down the hatches and you often got slaughtered for being negative even though you found it almost impossible to get out of your own half.
"Having said that, there were occasions when we went to Ibrox feeling we could get a result and we certainly did the day Allan Johnston scored his hat-trick in a 3-0 win. I don't know if I was pinching myself that day but I'm sure 'Magic' was at the end of the 90 minutes as his contribution that day was pretty special.
"Hibs have already gone to Ibrox and won well this season and there's certainly a chance that you can go through there and catch them on an off day.
"Hearts are also going well at the moment, which is important going into these games. Zaliukas has come in at the back and steadied the ship, while Kello is also doing well, looking as though he's the goalkeeper Hearts have been needing since Craig Gordon was sold.
"Ian Black is coming on to a game, too, and then, of course, there's the huge change in the striking department. There were some occasions in recent seasons when I don't think Hearts even played with a striker but now the gaffer's got great options in big Kyle, Stephen Elliott, Callum Elliot and Gary Glen, the latter being a player I certainly wouldn't be writing off even though he's not getting a game at the moment."
Having kept in touch with Locke, now first-team coach at Tynecastle, Fulton is well aware of the team spirit that's been re-ignited by Jefferies, the man he still calls gaffer even though it's been six seasons since that was actually the case.
Having played for him at three different clubs, Fulton probably knows better than most how long Jefferies, who has just turned 60, will want to remain in the game - and he doubts it will be as long as the man down at Manchester United.
"The fact the gaffer and Billy have never been out of work for long tells its own story," he remarked. "They're very good at what they do and, equally important, they also love being involved in the game.
"However, I don't think the gaffer will be around as long as Sir Alex - he loves the sun and will want to hit the beaches a lot quicker than Fergie!"