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The problem of signal design for bandwidth-efficient multiple access (BEMA) over additive white Gaussian noise (AWGN) channels is addressed under quality of service (QoS) requirements specified by asymptotic effective energies (AEEs). The AEE characterizes the bit error rate (BER) in the low-noise regime, but in contrast to BER, it is tractable and amenable to analysis and signal design. We adopt the BEMA strategy of bandwidth conservation where users are detected successively using minimum mean-squared error decision feedback (MMSE-DF) detection and where signals are designed in a greedy fashion for one user at a time, in the reverse order in which the users are detected. The signal design method proposed here is based on an exact characterization of how a signal update for one user affects the issue of preserving bandwidth with the addition of signals for subsequent users. A geometric insight in the construction of good signal sets and significant improvements in bandwidth over full-rank or orthogonal signaling are obtained. The main result of this paper can hence be seen as providing a tight upper bound on the minimum signature sequence dimension or rank (and hence bandwidth) needed to satisfy individual, possibly distinct user QoS constraints specified in terms of the AEE measure.