If success here is any indication of the state of British tennis, then something's heading in the right direction, and I'm not talking about Tim Henman. In the third round of the boys' singles, no nation had more players remaining than Britain's three: Miles Kasiri, Andrew Murray and Jamie Baker.

While, obviously, there's a gigantic leap from juniors to seniors, having such a good representation in the last 16 can only be a positive.

Kasiri, a former student at my academy, made the junior Wimbledon final this year and I've seen two of his matches here. He's been controlling his temperament, which has been suspect in the past, and he's been playing within himself. His volleys need work, and his mental approach needs to stay on track, but he's making progress.

What also stands out is that Miles talked this week about not feeling as much pressure here as at Wimbledon. The American crowds are neutral towards him, which he sees as "fairer" and less demanding. I think there's something in there that British sports fans should digest: support more, expect less. Look at what that attitude has done for Henman abroad this year.

The women's singles semi-finals are scheduled for today, weather permitting. Lindsay Davenport was my tip for the title at the start of the tournament and she faces Svetlana Kuznetsova for a place in the final.

The Russian does not suffer from the kind of weak serve that undermines some of her compatriots, and most of her game is solid. She also moves well from a low foundation.

But I believe a couple of key factors will work in Lindsay's favour. One is her bigger serve. The second is that I've seen Kuznetsova become frustrated and rattled when she makes errors, and that will count against her one step from a Grand Slam final.

The only reservation I have against Lindsay is if the match goes beyond a straight-sets win - and a two-set win for Lindsay is my prediction - then Kuznetsova might have the edge in physical conditioning to make life tough in a third set.

In the other semi, I think Jennifer Capriati will beat Elena Dementieva by returning Dementieva's pat-a-cake second serve with the kind of purpose and positioning that most opponents don't use because they think simply returning the serve is fine. It's not. When you hit it back down the centre, Dementieva can use her powerful groundstrokes and decent all-court game to punish you.