Inject preferred equity. That equity would have a vote. A big vote. That gives direct influence.
That equity must have a preferred right to all returns. Existing shareholders would be blocked from any reward until the government was paid out.
A seat on the board. Or more than one. If there's a 50% stake, the government must control the board.
The chairmanship of the remuneration and audit committees.
A change in remuneration and incentive policies.
Keep the toxic debt on the balance sheets of the banks: these bankers need the incentive to help sort this stuff out whilst knowing they won't go bust. But in case they thought they'd got an easy option I'd be demanding a ratchet in my equity. If they understated the scale of the problem now or failed to address the issue the UK government would be getting a bigger stake for its money in that case.
Demand changes in bank reporting.
Demand everything be on the record: an end to off balance sheet finance
Demand profits be remitted from overseas to help pay the cost of the bail out.
Close down all tax haven / secrecy jurisdiction operations for just that reason as a condition of the investment.
End all political lobbying by these banks.
Tighten capital requirement ratios.
There's a final point: make sure the new non-execs are people who can carry through the process of change. Appoint people like Prem Sikka, seasoned MPs like Frank Field, old hands like Will Hutton, journalists like Larry Elliot. This is not the moment for 'jobs for the boys'. The scheme will not work without such people. Credibility requires it.