Your average police officer, or fireman or customs official probably gets paid a tiny amount of money per month maybe $30-$50. But as an official of the government they have the opportunity to levy "additional taxes" during their day to day life. That's why often you'll find such countries have thousands of official regulations which on the face of it make no sense, how can anyone get anything done legally with all these regulations? The answer of course is that these regulations merely exist to create opportunities for the relevant officials to "collect taxes". You pay the official directly, you don't need to comply.
And their superiors know, their superiors get a cut of every bribe, it feeds up the chain of command within the relevant organisations. The officers on the beat or the fire department official who checks building fire regulations collects the "taxes" for himself and his superior.
So when you talk about stopping corruption in these countries you've got to replace this system of "taxation" with a real one that works. But that's easier said than done because the real corruption (fuelled by greed) also exists here and no one in their right mind is going to pay serious tax money to their government because it will disappear never to be seen again.
I can't claim that I know what the solution is to that, I thought I'd just put a different perspective on it.