Deep Text-to-Image Synthesis (TIS) models such as Stable Diffusion have recently gained significant popularity for creative text-to-image generation. However, for domain-specific scenarios, tuning-free Text-guided Image Editing (TIE) is of greater importance for application developers. This approach modifies objects or object properties in images by manipulating feature components in attention layers during the generation process. Nevertheless, little is known about the semantic meanings that these attention layers have learned and which parts of the attention maps contribute to the success of image editing. In this paper, we conduct an in-depth probing analysis and demonstrate that cross-attention maps in Stable Diffusion often contain object attribution information, which can result in editing failures. In contrast, self-attention maps play a crucial role in preserving the geometric and shape details of the source image during the transformation to the target image. Our analysis offers valuable insights into understanding cross and self-attention mechanisms in diffusion models. Furthermore, based on our findings, we propose a simplified, yet more stable and efficient, tuning-free procedure that modifies only the self-attention maps of specified attention layers during the denoising process. Experimental results show that our simplified method consistently surpasses the performance of popular approaches on multiple datasets.