The best, it turned out, meant putting Sofie on a new type of ventilator imported from America, which was being tested at the hospital.
Her parents say they were unaware that the treatment was experimental and that Sofie was being included in a trial. She did not do well. Brain damage was diagnosed. The Henshalls said a specialist dated its origin to the period she spent on the machine. By the age of two it was clear she would be permanently disabled.
It was the second tragedy to strike the family. In February 1992, Sofie's sister, Stacey, had been born prematurely and also with breathing problems. She had been on the same ventilator but she had died.
The questions for the inquiry ordered by the Health minister Baroness Hayman are expected to be what the parents were told about the trial, whether it was properly approved and monitored by the hospital's ethics committee and whether it was allowed to continue after it should have been obvious many babies were dying or being permanently injured.
Carl and Debbie Henshall assumed that the double tragedy which struck their family - they have six other children who are well - was due to the girls' prematurity, which they knew carried high risks. But they also believed that they had received the normal care given to any premature baby.
They say they did not know they were part of an experiment involving 122 babies treated between 1989 and 1993, of whom 43 died or suffered brain damage.
The Henshalls declined to talk about their experience ahead of giving evidence to the inquiry ordered by Lady Hayman.
But in earlier interviews they were angry and dismayed at the way they claim they were kept in the dark.
In 1997 Debbie said: "I believe that if both our girls had been given the normal treatment for breathing difficulties Stacey would be alive today and Sofie would be happily running around. Babies shouldn't be treated as pieces of meat."
The experiment, led by Professor David Southall and Dr Martin Samuels, was designed to see whether there was a better way of helping premature babies breathe than the standard method of inserting tubes down their throats and blowing air into their lungs under "positive pressure", which sometimes caused rupture of the immature tissues.
Instead babies were placed in a low-pressure chamber like an old iron lung, with a seal around their necks, which inflated their lungs by a technique known as "continuous negative extra-thoracic pressure" (CNEP), avoiding the need to insert tubes down their throats.
But a report of the trial published in the US journal Pediatrics in December 1996 noted differences in the blood flow through the brain in the CNEP- treated babies, visible on ultrasound. The ventilators are no longer used for premature babies but are still used for older infants.
The Henshalls said the first they knew that their daughters had been involved in an experiment was four years later when they consulted a specialist in Leeds who told them about the trial. They said the new treatment was offered to them as the safest, gentlest option in contrast to the "horrors" of the conventional option.
"We felt damn lucky. It was literally sold to us," they said. They are now considering legal action against the North Staffordshire Hospital Trust, as are five other couples. They are among 18 families who have complained to the General Medical Council.