IT may be the case that Scotland have still to win a game since qualifying for the World Cup finals - this was their third successive draw following defeats from France and Denmark - yet manager Craig Brown arrived home yesterday more confident than he was when heading into the European Championship finals two years ago.

Then the Scots had gone to the United States for preparatory games - interestingly enough against the same opposition as this summer - but they returned home nursing bruised egos after losing to the USA 2-1 in Connecticut and then to Colombia by the only goal of the game in Miami.

Now Brown's men come home without losing either of their games and the international team manager admits to ''cautious optimism'' about the matches in France.

After this draw against the United States he claimed: ''We are in better shape now than we were when we were going to England and the finals there two years ago.

''I think the pattern of play has improved and the results have improved, too, of course. What you have to remember is that we were playing two of the other countries who have qualified for France and this was the United States' big send-off before they leave for the finals.

''They wanted to give their supporters a win and we prevented that - and we had good chances to win the game in the second half.''

There were 46,037 fans in the RFK Stadium early on Saturday afternoon for the game and while hundreds of Scottish flags fluttered bravely in the Washington heat to testify to the Tartan Army's constant presence, the huge majority of the crowd were Americans there to wish their team well - and they left disappointed as Scotland's players dropped into the possession play which had surprised Colombia and which left the USA team frustrated for long spells as they attempted to find a way into the match.

The temperature in the stadium affected the players on both sides, with the USA coach Steve Sampson revealing later that on some occasions it soared to over 100 degrees on the pitch.

Yet the Scots coped well and Brown was particularly pleased with the way his strike force responded to the demands placed upon them.

''A few of the players were taken by surprise at to just how hot it was,'' he explained, ''and I wondered how they were going to handle it.

''The two lads up front, Kevin Gallacher and Darren Jackson, were magnificent. Kevin lasted more than 80 minutes before I took him off and he was flat out with illness for four days when we first arrived.

''Darren gave us a great shift, too, and then we also saw Christian Dailly making a superb long run from his own half to set up a chance for Kevin halfway through the second half.

''We want to see more of that from Christian, because he has pace and we want to convince him that he should use it more often in the wide position we have been playing him.''

The best openings for Scotland came after half-time, when they raised their game after Brown had encouraged them in the dressing room to be more offensive. His words worked so well that they forced two corners in the opening minutes after the interval.

Then, in 59 minutes, Jackson lofted a ball over the American defence and Gallacher raced clear - but so clear was he that he hesitated, looked towards the linesman anticipating an offside flag, and by the time he resumed his charge on goal he had lost his concentration. When the keeper, Kasey Keller, came off his line, the Blackburn striker struck the ball against him and the chance was lost.

The second opportunity arrived in the seventieth minute from that Dailly run which had so excited Brown. The wide player broke forward and made an opening for Gallacher, and again the striker saw his try easily stopped by Keller.

There was another occasion six minutes from the end when Craig Burley, who had replaced Billy McKinlay in the seventy-third minute, went beyond the United States' defence and then saw his cut-back held by the keeper.

Brown stressed afterwards that Gallacher had trained less than the others because of his illness, saying: ''He is not yet at the same level of sharpness as the other lads who have trained since we got here and who had also played in that first game.

''But that will come. I have to emphasise that we want to peak at the right time - when we are in France. And I'd rather have Kevin scoring two goals against Brazil than against the USA.''

The manager had tweaked the tactics a little, using John Collins in a slightly different role while playing two holding players in Paul Lambert and Billy McKinlay alongside him. Later, in the second half, he moved Collins into the role he prefers.

''He fancied trying the little change,'' Brown explained, ''but it didn't work as well as we had hoped.

''But we found other options for the midfield again, though you can take it that the back three are the men who will face Ronaldo and company, and that Jim Leighton will be in goal.

''And we were pretty close to the team for the opening game at parts of the game today.''

The implication there was that Craig Burley may be preferred to Billy McKinlay in midfield and that the wing backs could be Jackie McNamara and Christian Dailly.

McNamara took over from Tosh McKinlay after an hour, allowing Dailly to move to the left flank, where he had been a success against Colombia.

There will then be the question of whether Gordon Durie, out of the weekend game through injury, or Jackson will partner Gallacher up front.

Brown will tinker in training but he now has the style of play he wants and he said: ''That is the way the modern game is played at this level.

''It is essential to keep possession as much as possible. I think, by changing the philosophy a little and being able to get a couple of decent results here, the players are believing in what we have been working on and there has been a boost for morale.''

The only concern was that the Scots collected three bookings from the Mexican referee. Calderwood, for a tackle on Tab Ramos, and then Boyd and Jackson after clashing angrily off the ball with Preki Radosavljevic, who had begun the trouble and who escaped without a warning. However, a similar flare-up in France would be fatal.

There was a further boost, though, for the Scots from the American coach, Sampson, who claimed: ''I believe that Scotland will take a lot from coming over here and going away with a tie against Colombia and now a tie against us.

''Like all teams at this stage they will be happy to return home without injuries. They impressed me more than they did two years ago.''

That, as Brown remarked, had been the object of this latest expedition across the Atlantic.