Former 'Sun' journalists Ben O'Driscoll and John Troup, ex-managing editor Graham Dudman and current picture editor John Edwards were cleared by a jury at Kingston Crown Court on Friday.
But the jury is still deliberating over other counts faced by O'Driscoll and Dudman, and two other men.
The charges relate to paying police officers and prison guards for stories.
The three-month trial, presided over by judge Richard Marks QC, will resume on Monday.
Prosecutors have claimed that the men conspired to pay officials from 2002-11, including police, prison officers and soldiers.
They were arrested as part of Operation Elveden, Scotland Yard's investigation into corrupt payments to public officials.