"Arnie", or "Aldo", who previously worked with Roy Hodgson at Blackburn, is being employed as a fitness coach until the end of August, by which time a gamble in entering the Intertoto Cup will either have paid off with a place in the Uefa Cup, or will look like a bad misjudgment.
If it succeeds, West Ham will have played 10 matches in six weeks, but will still be two games behind almost everyone else in the Premiership. If they fail to come through the three two-leg rounds, even Redknapp admits: "It wouldn't be worthwhile".
Hence the importance of Longaretti's role in bringing the players to peak fitness unusually early. As competitive football got underway on Saturday, even before the school holidays had started, it did not require the observational powers of an expert to note how badly the home side faded after half-time, or why. They had been back in training for only 10 days - a surprisingly short time, given the importance being attached to this competition by a club long smitten with European football but starved of it for 18 years.
Jokerit, for all their limitations, are in the middle of the Finnish season and are therefore far better equipped to cope with a rush of games and Saturday's heat. Briefly bemused by the ball skills of Joe Cole and Paolo Di Canio, as Paul Kitson headed a smart goal and Trevor Sinclair hit the inside of a post, they realised soon after half-time that their vaunted opponents were not just running out of steam but clanking to a halt.
Mika Nenonen, a Finnish Under-21 international midfielder, broke past labouring defenders three times in the last 20 minutes, twice forcing Craig Forrest to save and once curling a shot past the post.
Redknapp must hope his team are sharper, as they should be, by Saturday's return game, in which success would mean a second-round tie against Hammarby, of Sweden, or Heerenveen, of the Netherlands.
Despite having Rob Jones from Liverpool on an extended trial, he would still like to reinforce his defence, if possible with the return of Everton's Slaven Bilic. Steve Potts, deputising for the injured Ian Pearce on Saturday, broke his nose, while Marc-Vivien Foe, having unexpectedly turned down the chance to join Liverpool, has suffered a bout of malaria.
Wanchope's arrival should make football's East Enders one of the most attractive teams in the country going forward - "we'll need three balls", Redknapp said - but there may not be many goals left in television presenter and male model Ian Wright, an ineffectual substitute against Jokerit, who yesterday suggested that this might be his final season.
Goal: Kitson (18) 1-0.
West Ham United (4-3-1-2): Forrest; Potts (Wright h/t), Ferdinand, Ruddock, Minto; Lampard, Lomas, Sinclair (Keller, 60); Cole; Di Canio, Kitson. Substitutes not used: Moncur, Abou, Coyne, Carrick, Bywater (gk).
Jokerit (4-5-1): Laaksonen; Rasanen, Hyrylainien, Holmgren, Tuunainen (Paavola 37); Helin, Roiko (Rantanen, 61), Nenonen, Koskela (Pylkas, 80), Viren; Sumiala.
Substitutes not used: Hiukka, Lehtinen, Yla-Jussila, Heikurainen (gk).
Referee: M Liba (Czech Republic).
Bookings: West Ham: Lomas. Jokerit: Rasanen.
Man of the match: Cole.
Chris Sutton and Didier Deschamps made their debuts for Chelsea on Saturday in a 1-1 draw with Birmingham City. Sutton, signed for pounds 10m from Blackburn this month, made little impact and was replaced at half-time by Tore Andre Flo. Gianfranco Zola was on target for Chelsea, who were denied victory by Birmingham central defender Michael Johnson, who scored seven minutes after half-time in front of 7,779 fans. Zola had pounced on a mix-up between his former Chelsea team-mate Eddie Newton and Birmingham midfielder Bryan Hughes to give the Premiership side a 26th-minute lead. Chelsea took off most of their big names as the match petered out into a draw.