With no goals conceded in the last three West Ham games providing the springboard for his first two competitive games for England again yielding clean sheets, Glenn wants the run to continue as long as possible.
The key, says Glenn, is the understanding he has with his defenders, and he explains: "There has been a consistency in the back four and we need to keep that together for as long as possible in the last seven games.
"I think that has helped David James and I noticed against Sunderland in the first half he came and took a couple of crosses cleanly and with a lot of confidence, which we hadn't always seen during spells this season.
"But when he had to take those crosses he did and then used the ball well.
"I have played with David James a long time ago when he first came into the Watford team as a teenage goalkeeper. I was in a back three with Barry Ashby and David Holdsworth and although we could handle ourselves on crosses David came and took those crosses - and I remember what a relief it was when you have got a 6ft 5ins goalkeeper coming out of the six yard box or even to the penalty spot at times.
"It was terrific because he would come and take those crosses nice and early, and it is a great relief for defenders when they see a goalie do that - and if you don't get out of the way you get clattered."
Glenn is keen to point out, however, that the good defending has not just been down to the defence, and he adds: "Since we started the good run the defending has hugely improved but I do feel there are lots of factors involved.
"If you start at the front there is a partnership that is working hard for the team closing defenders down and making them play it early so they are not always playing accurate balls.
"Because the front two are working as a pair the midfield four can get tight on their men, and if balls are played into their midfield they can be snapping straight away to win the ball back early.
"If the balls are then played into strikers when the midfielders of the opposing team are under pressure, the quality is probably not as good and our defenders can get tight and win a lot more balls.
"Just generally the whole team has defended so much better, and it has really been a team effort.
"The full backs have definitely had a positive effect on the two centre backs, and we couldn't be more delighted with the progress of Glen Johnson.
"And there is an equal amount of delight with Brevett who we took, not from Fulham's reserves, but from their first team - and let's not forget he saw off two new full backs that were brought to Fulham, not necessarily to replace him but to put him under more pressure, in Jon Harley and Pierre Wome, both quality left backs.
"He has settled in so, so quickly, and I think the full backs have allowed Pearce and Repka to concentrate solely on their job, and because of that they have done better while of course David James has benefited from the back four being settled as well.
"There was a doubt over Brevett's fitness for Sunderland but again he proved what a strong character he is by putting himself up and making himself available for the game, and like the other 10 he had an excellent game."