This paper presents a complete methodology for designing practical and highly undetectable steganographic systems for real digital media. The main design principle is to minimize a suitably-defined distortion by using efficient coding algorithms. The distortion is defined as a weighted difference of extended state-of-the-art feature vectors used in steganalysis, allowing the model used by steganalysts to be preserved, thus ensuring undetectability even for large payloads. The framework can be efficiently implemented even when the dimensionality of the feature set is larger than 10^7. High-dimensional models are necessary to avoid known security weaknesses, although they may be problematic in steganalysis. The paper introduces HUGO, a new embedding algorithm for spatial-domain digital images, which allows hiding 7 times longer messages with the same level of security compared to LSB matching. The paper also discusses the use of high-dimensional models in steganography, the importance of preserving image statistics, and the design of a new steganographic algorithm based on SPAM features. The security of the proposed scheme is experimentally verified, and the paper concludes that HUGO offers significantly higher security than traditional methods.This paper presents a complete methodology for designing practical and highly undetectable steganographic systems for real digital media. The main design principle is to minimize a suitably-defined distortion by using efficient coding algorithms. The distortion is defined as a weighted difference of extended state-of-the-art feature vectors used in steganalysis, allowing the model used by steganalysts to be preserved, thus ensuring undetectability even for large payloads. The framework can be efficiently implemented even when the dimensionality of the feature set is larger than 10^7. High-dimensional models are necessary to avoid known security weaknesses, although they may be problematic in steganalysis. The paper introduces HUGO, a new embedding algorithm for spatial-domain digital images, which allows hiding 7 times longer messages with the same level of security compared to LSB matching. The paper also discusses the use of high-dimensional models in steganography, the importance of preserving image statistics, and the design of a new steganographic algorithm based on SPAM features. The security of the proposed scheme is experimentally verified, and the paper concludes that HUGO offers significantly higher security than traditional methods.