And with Cardiff Blues travelling to Ravenhill on Friday night, Solomons is also wary of a side that has recently hit form.
Cardiff Blues are a very good side and with players like Ben Evans and Craig Quinnell bringing great experience to the team it will be a very tough game for us, said Solomons.
The Blues had a huge win over the Ospreys at the weekend. The Ospreys are a quality team and that win will have done a power of good for the confidence of the Blues. We know they will be really up for the challenge.
It is nice to be top of the Celtic League but we are keeping things in perspective. We are not even one third of the way through the competition and none of the sides are at full strength yet.
We are keeping our feet firmly on the ground - the tournament is very much still in its ascendancy at this stage. We are happy with where we are and with the fact that the youngsters have all had plenty of opportunities but this competition has a long, long way to run.
But the manner of the victory over Edinburgh Rugby, including denying the free-scoring Scots a try, did satisfy Solomons.
I was very pleased for the guys - it was one of those days when it ended up with most things going for us, he said.
We gave away too many penalties and made too many mistakes in the first half but we were much, much better after the break. We dominated possession and scored some very good tries - it was a great result for us.But we haven't had a game in the Celtic League yet where we have felt we have been totally on top - we know there are no easy games in this tournament.
Celtic League Fixtures.
Friday, 31st October.7.05: N-S Ospreys v Connacht, St Helens, David Changleng - (S) BBC/TG47.30: Glasgow v Leinster Lions, Hughenden, Nigel Owens (W)7.30: Munster v Celtic Warriors, Thomond Park.7.30: Ulster v Cardiff Blues, Ravenhill, Martin Changleng (S).
Saturday, 1st November.2.30: Llanelli Scarlets v The Borders, Racecourse Ground, David Keane (I)6.00: Gwent Dragons v Edinburgh, Rodney Parade, Olan Trevor (I)
Leinster V Glasgow Rugby.Date: Friday 31st October, 2003Kick-Off: 7.30pmVenue: Hughenden, Glasgow. Leinster.15: Gordon D'Arcy14: John McWeeney13: James Downey12: David Quinlan11: Gary Brown10: Matthew Leek9: Brian O'Meara1: Emmett Byrne2: Gavin Hickie3: Peter Coyle4: Aidan Kearney5: Ben Gissing6: Niall Breslin7: Shane Jennings capt8: Des DillonReplacements:16: Niall Treston17: David Blaney18: Ciaran Potts
Ulster v Cardiff Blues.Date: Friday October 31st 2003.Kick-off: 7.30pmVenue: Ravenhill, Belfast. Ulster. 15: Bryn Cunningham14: James Topping13: Ryan Constable12: Shane Stewart11: Tyrone Howe10: Adam Larkin,9: Kieran Campbell1: Bryan Young2: Matt Sexton3: Rod Moore4: Matt Mustchin5: Matt McCullough6: Andy Ward capt7: Neil Best8: Tony McWhirter.Replacements 16: Paul Shields17: Ronnie McCormack18: Rowan Frost19: Roger Wilson20: Reece Spee21: Seamus Mallon22: Scott Young