Side-informed steganography is a term used for embedding secret messages while utilizing a higher quality form of the cover object called the precover. The embedding algorithm typically makes use of the quantization errors available when converting the precover to a lower quality cover object. Virtually all previously proposed side-informed steganographic schemes were limited to the case when the side-information is in the form of an uncompressed image and the embedding uses the unquantized DCT coefficients to improve the security when JPEG compressing the precover. Inspired by the side-informed (SI) UNIWARD embedding scheme, in this paper we describe a general principle for incorporating the side-information in any steganographic scheme designed to minimize embedding distortion. Further improvement in security is obtained by allowing a ternary embedding operation instead of binary and computing the costs from the unquantized cover. The usefulness of the proposed embedding paradigm is demonstrated on a wide spectrum of various information-reducing image processing operations, including image downsampling, color depth reduction, and filtering. Side-information appears to improve empirical security of existing embedding schemes by a rather large margin.