What could a new PFI look like?

The Private Finance Initiative (PFI) was responsible for funding 694 projects across the UK. Initially loved by markets, hated by the left, and the doyenne of the centre, its gloss faded over time. Project failures and continuing bad publicity made it a problem for Government, while project disputes, especially in the NHS, made it unpopular with banks and investors.

And yet, calls to bring it back are increasing in volume.  So how do we create a new PFI which is better than the original?