On top, his £2million signing from Portsmouth, Nigel Quashie, tweaked knee ligaments in training on Thursday. He might finally have had a good night's kip last night.
Redknapp's opposite number, Rafael Benítez, is still going through torment, however. Fiercely criticised for fielding the weak team who lost away to Burnley in the FA Cup, a stronger one, showing eight changes, was well beaten at St Mary's. On this evidence, they will do well to survive in the second leg of their Carling Cup semi-final against Watford this week, even though they are a goal up. An injury to Sami Hyypia yesterday has not helped their cause, given the vulnerability of those around him.
Goals by David Prutton and Peter Crouch in the first quarter of the match were comfortably enough to bring Redknapp's first win - and Saints' third in the league this season - in his eighth game in charge. It helped that Liverpool were so lame and defensively poor. 'Big, big result for us,' said Redknapp. 'Today we might have turned the corner.'
Big, big result for Liverpool, too, with Everton seeing their hold on the important fourth place unchallenged by their city rivals. 'I am sure the fans will be disappointed,' said Benítez, seeking to reassure. 'The only thing I can say is that we will work harder and fight all the time.'
They need to. But while those qualities are admirable and the minimum requirement, the frailty in defence, with Mauricio Pellegrino a liability, and the absence of incisive quality farther forward will be more worrying to Liverpool fans. Fernando Morientes, anonymous yesterday, needs more time, but otherwise the Spanish contingent, the injured Xabi Alonso apart, have not impressed.
Redknapp got his game plan right. In the absence of the injured Kevin Phillips, he stretched five across midfield and left the willing, effective Crouch to forage alone up front, Prutton asked to break quickly in support. It helped Saints that Steven Gerrard looked to be feeling the effects of his groin injury and was nowhere near his usual driving self.
Saints gleaned instant dividends. Stephen Warnock allowed Mikael Nilsson to escape on the right and send in a cross that Hyppia played to the dallying Pellegrino, who allowed Prutton to rob him and play a one-two with Crouch before clipping a shot under Jerzy Dudek.
Warnock again went walkabout for Southampton's second and Jamie Redknapp, maturely dominant in a holding midfield role, found Prutton in space wide on the right for a cross to the far post, where Crouch shook off Jamie Carragher to head home.
It might have been worse for Liverpool before half-time, Crouch sending Prutton in for a run on goal past the exposed Hyypia, but his chip was straight at Dudek.
The hapless Warnock was spared further punishment by being withdrawn at half-time and for a while, Liverpool improved for Florent Sinama Pongolle's presence. Shots from Milan Baros, just wide, and Gerrard, grazing the bar, promised better. For a while, Saints grew twitchy, unaccustomed to the luxury of such a lead, but they need not have worried because a frustrated Liverpool resorted to wayward shots from long range.
Now Redknapp can prepare more restfully before the raucous FA Cup tie against his old club Portsmouth on Saturday. For Benítez, there will be no sleep till Watford. 