A conveyor system and methods for conveying and unstacking flat and non-flat packages. The conveyor system includes an inclined conveyor belt delivering packages to a tilted conveyor belt that conveys flat packages along its length while non-flat packages tumble off its lower side edge to initially cull flat packages from a bulk flow of packages. Retention means, such as a high-friction outer conveying surface or a raised barrier along the length of the outer conveying surface of the tilted conveyor belt, holds flat packages on the tilted conveyor belt. The inclined conveyor belt has stop elements spaced apart along the belt's length and is advanced in stop-and-go fashion to help unstack piggy-backed packages as they are conveyed up the incline. The initially separated packages are more fully culled in a conveyor comprising a roller conveyor belt with package-supporting belt rollers rotated in a direction to push packages sidewise toward a culling element that extends along the length of the roller conveyor belt.