Reversible Data Hiding is a form of Steganography, in which embedded information is recovered at the destination without any distortion with respect to information as well as cover media. This paper proposes a novel technique which deals with embedding data into encrypted images and recovering back the data as well as image without any distortion. Proposed technique also separates data embedding and image encryption steps. Person having only data hiding key can embed and extract the embedded data without the knowledge of encryption key. Room required to hide data is created before image encryption by estimating values of some randomly selected pixel positions. Improved histogram sifting method is used to hide data into the estimating errors of randomly selected pixel locations. Data is embedded with data hiding key. These estimating errors and remaining image pixel points are encrypted with standard encryption algorithm like AES (Advanced Encryption Standard). To encrypt estimating errors special encryption technique may be used. Proposed technique yields in complete reversibility