However, Rusedski has returned to training this week, although his spokeswoman Sharon Park is remaining cautious.
British number two Greg Rusedski was knocked out in the first round by Pete Sampras.
Henman has tumbled to 28th, with British number two Greg Rusedski just a spot behind in 29th.
The big serving Rusedski required just 67 minutes to defeat the third seed 6-4 6-4 in Nottingham.
Koubek beat Greg Rusedski in the decisive rubber to relegate Britain from the Davis Cup World Group.
BBC: Koubek claims he did not knowingly take banned substances
Rusedski's contemporaries on the ATP Tour were also surprised by the news that the Briton had tested positive.
Greg Rusedski's retirement after the weekend win over the Netherlands has opened up a free spot on the team.
BBC: Jamie Baker is among those challenging for a Davis Cup spot
Rusedski will face Jonas Bjorkman in Friday's semi-final after the Swede made light work of Russia's Andrei Stoliarov .
Great Britain's main weakness has always been an over-reliance on Henman and Rusedski.
Greg Rusedski falls one place to 42nd after his first round defeat by former world number one Pete Sampras.
The high spot of big-serving Rusedski's career so far has been reaching the final of the US Open in 1997.
And with Greg Rusedski also struggling with fitness, Henman will be expected to prove his commitment to the British cause.
Rusedski has not played since the US Open in September, and recently split from coach Sven Groeneveld for a second time.
If Rusedski can beat Waske, he is likely to face American Andy Roddick in the second round at the All England Club.
"I'm really pleased with the way I played, " said the 29-year-old Rusedski.
Rusedski will face Belgium's Olivier Rochus in the second round on Wednesday.
Henman's Hill, sometimes dubbed Rusedski Ridge, became Hewitt Hill on Monday as the defending champion walked out to open play on Centre Court.
Smith, who won the job ahead of candidates including former world No. 4 Greg Rusedski, worked with Murray while he was a junior player.
CNN: Djokovic dumps coach Martin ahead of Monte Carlo campaign
Another boost for Rusedski was the defeat of Germany's Alexander Waske , his first-round opponent at next week's Wimbledon, by Younes El Aynaoui .
Jamie Baker and Alex Bogdanovic both lost in their first-round matches on Tuesday, while Greg Rusedski and Martin Lee were defeated the day before.
Crowther insisted that while Lloyd may have worked well with Henman and Rusedski, his behaviour as captain had had an adverse effect on fringe players.
But the retirement of Rusedski, who partnered Murray in the doubles, leaves a gap and Lloyd has called on the younger players to take advantage.
BBC: Jamie Baker is among those challenging for a Davis Cup spot
Hopes of an all-British final in the Samsung Open were dashed when Arvind Parmar , who might have played Rusedski, bowed out in the quarter-finals.
Rusedski must beat Nikolay Davydenko in round two to overtake Henman.
When Rusedski lost his serve in the second game of the second set, to trail 3-0, he looked to be on the verge of going out.
Meanwhile, former Davis Cup player Barry Cowan is in no doubt that if Rusedski is found to have taken illegal drugs, then he should be banned.
The ATP has refused to comment on Greg Rusedski's positive test for the banned substance, but insists it will enforce any punishment meted out to the player.
"Beating Roddick would help to open up the draw as he is the fifth seed, but you have to look at his performance at Queen's, " added Rusedski.
Teenage star Murray continued to show courage beyond his years as he and Rusedski regained the initiative after going a break down early in the third set.
Only six of the 16 seeds remained heading into this third round after a series of shocks including defeats for British pair Tim Henman and Greg Rusedski.
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