Parameter-embedded watermarking is effected through slight perturbations of parametric models of some deeply-integrated dynamics of the speech signal. In set-membership filtering (SMF) based parametric watermarking, linear predictor (LP) coefficients of the original speech are modified subject to an objective fidelity constraint. SMF is used to obtain sets of allowable parameter perturbations (i.e., watermarks) subject to a constraint on the error between the watermarked and original material. This paper discusses the robustness of SMF based watermarking to filtering, quantization and combination attacks. An important consideration in watermark robustness is the energy of the watermark signal (difference between watermarked and original signals). The most robust watermark is obtained from perturbed LP coefficients at the boundary of the membership set. A constrained optimization problem is solved to obtain the best watermarks for filtering and quantization attacks