I have (just) selected not to receive any more paper statements from AmEx and emailed Barclaycard asking if there was the same facility.
Their response was:
'Unfortunately we are unable to stop sending out paper statements by post.
As a financial institute, we are legally bound to send hard copy statements to all cardholders if there is a balance owing on their account.'
Other cards have paperless statements (Accucard)? As well as online savings accs, so why can't they do it (assuming they have my permission), when I am sure they want to (to save on the postage etc) when others can?