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Because we are naturally prejudiced about the validity of both the reservoir pressure ($P_{res}$) and instantaneous wave-free ratio (iFR), having been involved in the conception and development of both ideas, we will try to present our arguments as transparently and fairly as possible. As far as possible we will demonstrate the errors by direct quotations from the paper. The whole paper is available from the Hypertension web site\href{http://hyper.ahajournals.org/content/early/2015/05/26/HYPERTENSIONAHA.115.05567.full.pdf}{} and should be consulted directly if there are any questions about our treatment of the text.  Approximately two thirds of the paper is taken up with a discussion of wave separation and wave intensity from the point of view of the more usual Fourier-based methods of analysing cardiovascular mechanics, frequently called the impedance method. This part of the paper is, as far as we can see, both insightful andlargely  free of major  errors. We found some of the discussion about wave intensity analysis thought-provoking and agree with most of their conclusions. We recommend the first two-thirds of this paper to anyone interested in arterial mechanics. In contrast, the last third of the paper, starting with the final sentence of the section 'Summary of Wave Separation and WIA' is riddled with errors of interpretation and, more importantly, contains a number of mistakes (or in Darwin's terms 'false statements of fact') that need to be corrected. Instead of dealing with these errors chronologically, we will point out the fundamental errors first and then deal with their sequelae. 
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