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Following heart transplant (HT), the patient's heart functions under complete cardiac denervation. As a result, the variability in physiologic signals is extremely reduced. We have previously reported that in addition to the typical spectral components (of very low amplitude), part of the HT patients (above 50%) demonstrated unexpected additional peaks in their heart rate and blood pressure spectra. These peaks may be a result of the development of compensatory mechanism induced by loss of parasympathetic control, or of increased importance of nonlinear control interactions. It is important to quantify these strange, unexpected very-high frequency (VHF) peaks, to understand their origin and their contribution to cardiac control in transplant patients. In this paper, we chose to examine these VHF peaks by applying the bicoherence approach. The reduced signal to noise ratio, occurring in these patients, results, however, in an extremely noisy bicoherence. We, therefore, developed several statistical tools in order to distinguish between "true" bicoherence peaks (reflecting true phase coupling) and spurious peaks. The outcome of these methods was an efficient and sensitive bicoherence thresholding procedure, able to identify most of the spurious peaks. Applying these tools to the bicoherence of cardiovascular signals which display VHF peaks, revealed several significant bicoherence peaks. Interestingly, these peaks consisted of two different types. The first type of VHF peaks simply reflects nonlinear cardiac-respiratory coupling, imposed by nonsinusoidal breathing. The second type, however, is clearly not induced by the respiratory system. We believe that these type-2 VHF peaks reflect the evolution of a new, yet unexplained, compensatory mechanism.