Embedding the l1 norm in gradient-based adaptive filtering is a popular solution for sparse plant estimation. Supported on the modal analysis of the adaptive algorithm near steady state, this work shows that the optimal sparsity tradeoff depends on filter length, plant sparsity and signal-to-noise ratio. In a practical implementation, these terms are obtained with an unsupervised mechanism tracking the filter weights. Simulation results prove the robustness and superiority of the novel adaptive-tradeoff sparsity-aware method.