Combinations of novel pulse-echo acquisitions and clutter filtering techniques can improve the sensitivity and the specificity of power Doppler (PD) images, thus reducing the need for exogenous contrast enhancement. We acquire echoes following bursts of Doppler pulse transmissions sparsely applied in regular patterns over long durations. The goal is to increase the sensitivity of the acquisition to slow disorganized patterns of motion from the peripheral blood perfusion. To counter a concomitant increase in clutter signal power, we arrange the temporal echo acquisitions into two data-array axes, combine them with a spatial axis for the tissue region of interest, and apply 3-D singular-value decomposition (SVD) clutter filtering. Successful separation of blood echoes from other echo signal sources requires that we partition the 3-D SVD core tensor. Unfortunately, the clutter and blood subspaces do not completely uncouple in all situations, so we developed a statistical classifier that identifies the core tensor subspace dominated by tissue clutter power. This paper describes an approach to subspace partitioning as required for optimizing PD imaging of peripheral perfusion. The technique is validated using echo simulation, flow-phantom data, and in vivo data from a murine melanoma model. We find that for narrow eigen-bandwidth clutter signals, we can routinely map phantom flows and tumor perfusion signals at speeds less than 3 mL/min. The proposed method is well suited to peripheral perfusion imaging applications.