There was a palpable sense of relief in the NHS when the name of its new chief executive was announced last week. Many may not have known much about David Nicholson, the man assigned to run the health service in London, until the call came for him to take over England as a whole. But that didn't matter. From the splendour of the Lutyens designed headquarters of the British Medical Association (BMA) in the Bloomsbury district of London to the humbler offices of Unison stewards across the land, reassurance came from the knowledge that this Nicholson is an NHS man through and through, with 25 years' service to prove it.

Perhaps more to the point, he is not an American healthcare executive, blue in tooth and claw. There is no reason to believe that anti-US sentiment is deeper in the NHS than in other walks of life. But there was resentment attached to the expectation that Tony Blair would seal his plan to turn the NHS into a competitive market by putting an American in charge.

At one stage, that outcome looked probable. Two of the four names on the shortlist for the job hailed from across the Atlantic. One was Ken Kaiser, the former head of the US department providing healthcare for army veterans. The other is thought to have come from among the top brass at Mount Sinai medical centre in New York.

Imagine the hullabaloo if either had been chosen. Never mind the qualities that propelled them on to the shortlist. The selection of an American would have been interpreted as evidence that Blair thought nobody among the 1.3 million people employed by the NHS was fit to run it.

This Sven-Goran Eriksson moment did not come to pass. The civil service commissioners set up an interviewing panel of the great, including Sir Alan Langlands, a former NHS chief executive; Dame Carol Black, outgoing president of the Royal College of Physicians; and Sir Gus O'Donnell, the cabinet secretary.

Were they influenced by fear of damage to NHS morale if they picked either Yank - or the third external candidate, Ian Smith, chief executive of the UK private healthcare provider General Healthcare Group? Did the Americans lack eagerness after discovering the relative modesty of UK pay packets and the awkward truth that they would not be in supreme command of the NHS, since the health secretary, Patricia Hewitt, thinks she is? We may never know.

In the end, the panel probably relied on a hunch that Blair's yearning for an American was not as important as the need for the NHS to retain its self-respect. Blair had the power of veto, but didn't use it.

This fits with other signs that the government has begun to realise it cannot browbeat the NHS into a state of enthusiasm for reforms. Last week, Hewitt invited representatives of the BMA, Royal College of Nursing, Unison and Amicus to join NHS managers and regulators on a new health and social care reform advisory group. She appointed Andy Burnham, the health minister, as a communications troubleshooter to explain the reforms "consistently and positively" to staff and patients.

These conciliatory moves should not be interpreted as evidence that the government's zeal for reform is waning. It is still heading full pelt towards turning the NHS into a competitive market. But it may now be more ready to listen to good ideas for changing the programme without changing the direction.

So we are inviting readers to send their pragmatic suggestions, in no more than 150 words, to society@theguardian.com, flagging the entry "summer challenge". Entries should arrive before August 15. Pragmatic means improving the policy without it counting as a U-turn. Feel free to argue for more radical change. But, if you can't imagine Hewitt saying it in her speech to the Labour party conference in Manchester next month, you won't win the prize ... a bottle of wine. Don't worry. It won't be Californian.

· John Carvel is the Guardian's social affairs editor.