The problem of choosing parametric descriptions of the systemic vascular bed suitable for monitoring beat-to-beat changes in peripheral vascular properties is considered. Three simple models with two, three, and five elements are compared, essentially exploiting the Akaike information criterion combined with reasonable requirements for estimate accuracy. Analysis of pressure data, which are either simulated by the five-element model or measured on a mock circulatory system during abrupt changes in peripheral resistance, suggests guidelines for model selection. In particular, the five-element model exhibits very close adherence to physical reality by allowing for reflection, while the classical windkessel model provides the most reproducible estimates.