Relative cerebral blood flow (CBF) and tissue mean transit time (MTT) estimates from bolus-tracking MR perfusion-weighted imaging (PWI) have been shown to be sensitive to delay and dispersion when using singular value decomposition (SVD) with a single measured arterial input function. This study proposes a technique that is made time-shift insensitive by the use of a block-circulant matrix for deconvolution with (oSVD) and without (cSVD) minimization of oscillation of the derived residue function. The performances of these methods are compared with standard SVD (sSVD) in both numerical simulations and in clinically acquired data. An additional index of disturbed hemodynamics (oDelay) is proposed that represents the tracer arrival time difference between the AIF and tissue signal. Results show that PWI estimates from sSVD are weighted by tracer arrival time differences, while those from oSVD and cSVD are not. oSVD also provides estimates that are less sensitive to blood volume compared to cSVD. Using PWI data that can be routinely collected clinically, oSVD shows promise in providing tracer arrival timing-insensitive flow estimates and hence a more specific indicator of ischemic injury. Shift maps can continue to provide a sensitive reflection of disturbed hemodynamics.