Reducing money for American sailor after swindle (13)

'reducing' is the definition.
('concentrate' can be a synonym of 'reduce')

'money for american sailor after swindle' is the wordplay.
I cannot quite understand how this works, but
'money' could be 'cent' (eg denomination of dollars) and 'cent' is found within the answer.
'american' could be 'a' (common abbreviation - e.g. in organisation names) and 'a' is located in the answer.
'swindle' could be 'con' (synonyms) and 'con' is found in the answer.
This explanation may well be incorrect...

Can you help me to learn more?