Despite recent advancements in text-to-image models, achieving semantically accurate images in text-to-image diffusion models is a persistent challenge. While existing initial latent optimization methods have demonstrated impressive performance, we identify two key limitations: (a) attention neglect, where the synthesized image omits certain subjects from the input prompt because they do not have a designated region in the self-attention map despite despite having a high-response cross-attention, and (b) attention interference, where the generated image has mixed-up properties of multiple subjects because of a conflicting overlap between cross- and self-attention maps of different subjects. To address these limitations, we introduce CoCoNO, a new algorithm that optimizes the initial latent by leveraging the complementary information within self-attention and cross-attention maps. We first identify subject-specific regions from the self-attention map and term them attention zones. Our method then introduces two new loss functions: the attention contrast loss, which minimizes undesirable overlap by ensuring each attention zone is exclusively linked to a specific subject's cross attention map, and the attention complete loss, which maximizes the activation within these attention zones to guarantee that each subject is fully and distinctly represented. Our approach operates within a noise optimization framework, avoiding the need to retrain base models. Through extensive experiments on multiple benchmarks, we demonstrate that CoCoNO significantly improves text-image alignment and outperforms the current state of the art.