Safest way to get rid of aphids?

[Lazgaot]

I'm trying to overwinter a medium sized Scotch Bonnet chilli plant on my windowsill. Its relatively warm but not hot and I've only watered it sparingly. Unfortunately though its overrun with aphids and I've tried weak soapy solution (twice) to get rid of them. The plant has now lost all its leaves but has just started sending out new ones which are also covered in new aphids, as are all the soft growing points on the stems!!! I've tried to kill them one by one and to brush them off but need a more reliable solution. Any ideas?

[zazen999]

You need to squish every day as each day they lay more eggs......and if there is a nice sunny day, get it outside for a few hours - if it is a rainy day, spray with weak soft soap solution and get it outside - the weak soap clags up their breathing holes and the rain will help to suffocate them and wash them away. If it is a sunny day - then hopefully other insects will come along and have them for lunch. If they haven't gone when you bring it back in, then squish and look at it again the next day.

[Two_Sheds]

They really are a nuisance - and where on earth do they come from, in winter? (I've got them on young plants that have never been outside)

Keep squishing, every day, as Zaz says

[Lazgaot]

Aye aye, daily aphid popping it is then.