When Sollozzo entered the picture, he requested the Corleone for protection and to give up political influence, something that he did not need at large for his business - so he was pushing his and someone else's agenda -, in return he will give a cut of the profits, and take care of the Tataglia from his end. Thus at 'The Peace Meeting', A meeting to discuss peace between the Tataglias and the Corleones, there was no much talk about the family feud from anyone other than from Don Vito and Tataglia, instead Barzini took that opportunity to (once again) 1)request for the Corleone to give up judges and political influence and 2)push the Sollozzo business (trafficking and dsitribution of drugs), as he said: "Don Corleone has all the judges and the politicians in New York, and he must share them, he must let us draw the water from the well". And went on to say: "Traffic and drugs will be permitted but controlled, and Don Corleone will give up protection in the East and there will be the peace". Barzini set then the peace terms, he obtained what he wanted from that meeting, and Don Corleone had to give up a lot for relative peace and to have Michael returned safely, that is when the Don realized that the one orchestrating everything from the beginning was Barzini.