Information hiding techniques are currently increasingly utilized by cybercriminals for various nefarious purposes. That is why, from the defenders’ perspective, it is essential to investigate how such methods can be used to bypass security countermeasures so the countermeasures can be further improved. Thus, in this paper, we address the challenge of embedding secret data into network traffic while preserving the statistical properties of the carrier stream, particularly Shannon entropy. In particular, we focus on storage-based network steganography, and we introduce two novel embedding strategies that significantly reduce detectability by entropy-based network wardens. The first technique employs an inverse Huffman-inspired encoding scheme, which encodes encrypted secret messages in a way that closely mimics the entropy distribution of the cover traffic while maximizing bandwidth. The second method is designed to precisely match the entropy of the carrier traffic, allowing tunable trade-offs between stealth and bandwidth. Extensive experimental evaluations across synthetic and real-world network distributions demonstrate that the proposed schemes achieve superior performance in maintaining entropy while offering higher steganographic bandwidth than conventional techniques. This research advances the state of covert communications by quantifying entropy-bandwidth trade-offs and delivering practically implementable, entropy-aware embedding methods.