Despite recent advances in joint processing of images, sometimes it may not be as effective as single image processing for object discovery problems. In this paper while aiming for common object detection, we attempt to address this problem by proposing a novel QCCE: Quality Constrained Co-saliency Estimation method. The approach here is to iteratively update the saliency maps through co-saliency estimation depending upon quality scores, which indicate the degree of separation of foreground and background likelihoods (the easier the separation, the higher the quality of saliency map). In this way, joint processing is automatically constrained by the quality of saliency maps. Moreover, the proposed method can be applied to both unsupervised and supervised scenarios, unlike other methods which are particularly designed for one scenario only. Experimental results demonstrate superior performance of the proposed method compared to the state-of-the-art methods.