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Glenn Roeder has urged his players to end the season on a high note, beginning with a third successive Premiership win against Charlton Athletic on Saturday.
The Hammers boss knows that victory over Alan Curbishley's men at Upton Park could lift his team into seventh spot in the table - our highest league placing this season.
However, with the likes of Aston Villa, Tottenham, Charlton, Middlesbrough and Southampton also fighting for a top half finish, a couple of losses could easily signal a sudden drop into the lower reaches of the Premiership - a situation that Roeder is determined to avoid.
"We certainly won't be relaxing," says Glenn. "The time to relax is on your holidays, and they don't start for another month yet.
"We're aiming for seventh spot, but that is also the target of all the teams around us. It's certainly achievable and on Saturday we are playing one of the teams who are also going for that seventh spot, so it has hopefully got the makings of a good game.
"I don't know what the formula is for qualifying for Europe next season. There are lots of permutations, but I would just like to finish seventh and then see what happens.
"Now that we have reached the 40 point mark and ensured our Premiership status for next season, we can approach every game with confidence and belief, and really have a go for that seventh place.
"The important thing now is not to relax. I spoke to the players about it last week and told them that this is the most important month of the season, when the prizes are handed out. Seventh spot would be a real achievement for us, so we must treat it as our very own title race."
It certainly appears that the critics, who tipped the Hammers as relegation favourites at the start of the season and predicted a short stay in the managerial hotseat for Roeder, will be forced to eat their words, but the Hammers boss typically plays down the praise directed at him and insists his players deserve the credit.
"I've got to be honest, I feel that the players this year have done really well, considering the size of the squad and the job they have been asked to do," says Glenn. "We have already bettered last season's total and still have six games to play, so we want to get back to that top half finish we enjoyed three years in a row.
"The atmosphere among the players here is fantastic. Ask the likes of Trevor Sinclair and Steve Lomas - experienced players who have been here for a few years now - and they will tell you how much they are enjoying themselves. They all stick together and the team spirit is very strong.
"I always said the key to this season was going to be keeping a small squad fit and healthy. There have obviously been some problems, like the horrendous injury suffered by Don Hutchison, and one or two other fairly serious ones to David James and Michael Carrick, but generally I have had a settled squad to choose from and that has been very important."
Meanwhile, the Hammers boss looks set to name a virtually unchanged line-up from that which beat Ipswich and Fulham last weekend, with the exception being the left-back position.
"Vladimir Labant has severe bruising after his collision at Fulham and will miss out on Saturday, but Nigel Winterburn will be back in the frame after sitting out that game," reveals Glenn.
"Other than that, everyone is okay and there were no other injuries over the hectic Easter weekend. That is a big bonus at this stage of the season and hopefully we can keep it that way until the end of the campaign."