Roger Federer may yet hold on to his world No 2 position in time for the French Open, but Andy Murray has his ranking fate in his own hands this week.
Murray will return to No 2 if he goes further than Federer here at the Rome Masters and the Scot proved he is in good shape by beating Mikhail Kukushkin 6-3, 6-3 in his opening match.
Federer, nevertheless, also got off to a winning start, beating Alexander Zverev 6-3, 7-5.
Federer, who is still concerned about the back problem which forced him to withdraw from last week's Madrid Masters, replaced Murray at No 2 on Monday, but the Scot will be favourite to reclaim the position in time for the French Open, which begins in 11 days.
Federer is defending 600 ranking points this week as the runner-up here last year, while Murray is defending only 90, having withdrawn before the third round in 2015 because of fatigue after winning back-to-back titles in Munich and Madrid.
Murray would be certain to return to No 2 if he reached the final here, but there are plenty of other scenarios in which he would do so.
If Federer lost in the final, for example, Murray would need only to win one more match this week to overtake him.
Being No 2 will earn more than prestige.
It would also mean going to Roland Garros knowing that it would be impossible to face Novak Djokovic, the world No 1, before the final.
Djokovic, who won the Madrid title on Sunday, began his defence of the title here with a 7-5, 7-5 victory over France's Stephane Robert.
After his victory, Murray, who was competing in his first match since splitting from coach Amelie Mauresmo, said: "I served well. It's tough to get much of a rhythm, it's quite a breezy day. I didn't feel that comfortable from the back of the court."
Murray is not anticipating having a new coach in place for Roland Garros and will mull over whether to go for another high-profile former player or a more technical coach.
He said: "I haven't thought loads about it. The thing with the top players, the super coaches, is that experience around the major events and big matches, understanding the stress and pressure and how to deal with that.
"Passing on their experiences is something I've benefited from over the last few years with my last few coaches.
"But I made some technical changes on my serve over the last couple of months and that's made a huge difference to my game and taken my game up a level. The ex-players don't tend to be technical coaches so it's tough to pick."
Meanwhile, Heather Watson still has work to do if she is to achieve her main goal of 2016. The 23-year-old Briton has set her heart on playing at this summer's Olympic Games but after losing 6-4, 6-2 to Barbora Strycova in the second round here her place in the field for Rio is still in some doubt.
A ranking inside the world's top 60 by the end of the French Open should be enough to secure Watson's Olympic place, but the world No 55 could yet be overtaken by the cut-off date.
Johanna Konta claimed another top-10 scalp with victory over home favourite Roberta Vinci in the second round.
The British number one continued her remarkable season by seeing off the world number seven 6-0 6-4.
Konta was exceptional in the opening set, dropping just seven points and outclassing last year's US Open finalist.
Vinci stopped the rot after seven games and the second set was much more of a battle as a boisterous home crowd attempted to unsettle Konta.
But the 24-year-old held her nerve superbly to serve out the victory.