The singer, 24, checked into The Capio Nightingale Hospital in central London last week.
'She has been ill and is withdrawing but at least she is sticking with it as she detoxes,' says the pal,
'With her family's support we are hopeful that there is finally light at the end of the tunnel as she weans herself off drugs.
'She will stay in rehab for as long as it takes, even if it is 3 or 4 weeks. Nobody is saying it will be easy, but things are looking good at the moment and doctors are encouraged.'
But it's going to be a long haul - and Amy might be tempted back into her old ways as soon as she leaves the clinic.
'The classic way is for them to start doing drugs again then end up having to go back into rehab afterwards,' the pal tells The Sun.
'Nobody is sure what will happen but we are all keeping our fingers crossed that this stint does her good.'
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