I think that about 15-20 percent of the officials are perfectly honest, about 30-35 percent absolutely (and compulsively) corrupt and the rest 50 percent form the marginal category.
The marginal category has both kinds of people: one who can be honest (provided the leadership and laws are perfect) and others who aspire to be Billionaires (at the cost of . . .).
Now the solution is simple. Identify and execute the compulsive corrupts (This of course have to start from judiciary and police). For the marginal corrupts aspiring to be compulsive corrupts create a ministry called the Ministry of the Corrupt, Under-Performers and Responsibility-Shirkers (MOCUPARS). Transfer the dead weight to this ministry, advertise their posting here, give them work similar to jail inmates (Constitutionally and Legally they cannot refuse work) and telecast it on MOCUPARS Channel.
This exercise should be done fairly, not like that is practiced today where honest ‘hard to crack nuts’ are targeted while those guilty walk free.
I think this model can be applied to society as a whole, where a majority of people sit at the margins to make a fast buck but if properly motivated they can be good and honest citizens.
IMAGE FROM: http://www.icgg.org/downloads/CPI_2006_Map_1024px.png