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Electromagnetic (EM) fields have been extensively studied as potent side-channel tools for testing the security of hardware implementations. In this work, a low-cost side-channel disassembler that uses fine-grained EM signals to predict a program's execution trace with high accuracy is proposed. Unlike conventional side-channel disassemblers, the proposed disassembler does not require extensive randomized instantiations of instructions to profile them, instead relying on leakage-model-informed sub-sampling of potential architectural states resulting from instruction execution, which is further augmented by using a structured hierarchical approach. The proposed disassembler consists of two phases: (i) In the feature-selection phase, signals are collected with a relatively small EM probe, performing high-resolution scans near the chip surface, as profiling codes are executed. The measured signals from the numerous probe configurations are compiled into a hierarchical database by storing the min-max envelopes of the probed EM fields and differential signals derived from them, a novel dimension that increases the potency of the analysis. The envelope-to-envelope distances are evaluated throughout the hierarchy to identify optimal measurement configurations that maximize the distance between each pair of instruction classes. (ii) In the classification phase, signals measured for unknown instructions using optimal measurement configurations identified in the first phase are compared to the envelopes stored in the database to perform binary classification with majority voting, identifying candidate instruction classes at each hierarchical stage. Both phases of the disassembler rely on a four-stage hierarchical grouping of instructions by their length, size, operands, and functions. The proposed disassembler is shown to recover ∼97–99% of instructions from several test and application benchmark programs executed on the AT89S51 microcontroller.