Image and video processing in the encrypted domain has recently emerged as a promising research area to tackle privacy-related data processing issues. In particular, reversible data hiding in the encrypted domain has been suggested as a solution to store and manage digital images securely in the cloud while preserving their confidentiality. However, although efficiency has been claimed with reversible data hiding techniques in encrypted images (RDHEI), reported results show that the cloud service provider cannot add more than 1 bit per pixel (bpp) of additional data to manage stored images. This paper highlights the weakness of RDHEI as a suggested approach for secure and privacy-preserving cloud computing. In particular, we propose a new, simple, and efficient approach that offers the same level of data security and confidentiality in the cloud without the process of reversible data hiding. The proposed idea is to compress the image via a lossless image coder in order to create space before encryption. This space is then filled with a randomly generated sequence and combined with an encrypted version of the compressed bit stream to form a full resolution encrypted image in the pixel domain. The cloud service provider uses the created room in the encrypted image to add additional data and produces an encrypted image containing additional data in a similar fashion. Assessed with the lossless Embedded Block Coding with Optimized Truncation (EBCOT) algorithm on natural images, the proposed scheme has been shown to exceed the capacity of 3 bpp of additional data while maintaining data security and confidentiality.