Dual-axis swallowing accelerometry is an emerging tool for the assessment of dysphagia (swallowing difficulties). These signals however can be very noisy as a result of physiological and motion artifacts. In this note, we propose a novel scheme for denoising those signals, i.e. a computationally efficient search for the optimal denoising threshold within a reduced wavelet subspace. To determine a viable subspace, the algorithm relies on the minimum value of the estimated upper bound for the reconstruction error. A numerical analysis of the proposed scheme using synthetic test signals demonstrated that the proposed scheme is computationally more efficient than minimum noiseless description length (MNDL)-based denoising. It also yields smaller reconstruction errors than MNDL, SURE and Donoho denoising methods. When applied to dual-axis swallowing accelerometry signals, the proposed scheme exhibits improved performance for dry, wet and wet chin tuck swallows. These results are important for the further development of medical devices based on dual-axis swallowing accelerometry signals.