Singer Edwyn Collins is being treated for the MRSA bug after a surgical scar became infected.
Edwyn Collins had a global solo hit with A Girl Like You in 1995
The 45-year-old, who suffered two brain haemorrhages in February, is said to be responding to treatment for the bug at London's Royal Free Hospital.
His wife Grace Maxwell wrote on his website that the infection has been "very difficult to get under control".
Collins, who had hits with Rip It Up and A Girl Like You, required further surgery to remove infected scar tissue.
Mrs Maxwell also said: "I'm hopeful that we've turned a corner. Edwyn continues to feel quite well in himself."
It emerged that Collins has been suffering with the so-called "superbug" for some weeks.
A piece of bone which was replaced at the beginning of April had to be removed again after an infection was detected.
Collins (right) burst onto the music scene with his band Orange Juice
The former frontman of Scottish pop group Orange Juice had left the north London hospital to be treated at a rehabilitation centre, but returned a day later.
A statement from the Royal Free Hospital said: "Grace and the family would like to restate their enduring gratitude to staff for the lifesaving care they have given to Edwyn."
It added that "he continues to improve under the watchful eye of the medical team".
Collins was taken to hospital on 20 February, several days after complaining of vertigo and vomiting.
The Edinburgh-born singer-songwriter then had emergency surgery after suffering a second haemorrhage.
Collins led Orange Juice to a number eight UK hit with Rip It Up in 1983. His solo single A Girl Like You reached number four in 1995, and was a hit around the world.
A compilation of his early songs, The Glasgow School, is due to be released this month.