Many equilibrium models of freeway traffic relationships or ‘fundamental diagrams’ have been proposed, but some that appear plausible or convenient turn out unrealistic, and firm conclusions have not been reached. This paper aims to identify simple closed-form models most consistent with data, and some relevant properties. Eleven models of congested traffic flow, using only directly measurable parameters for portability, are evaluated against 24-hour one-minute-averaged cross-sectional data from several congested sites on a UK motorway, collected from MIDAS (Motorway Incident Detection and Automatic Signalling) loops. MIDAS records time-mean speeds, but space-mean speeds are considered necessary to ensure compatibility with the fundamental relationship of traffic. Proxy space-mean speeds are estimated using results from analysing NGSIM (New Generation Simulation) data, together with an independent model of speed variance, Wardrop’s formula, and estimates based on occupancy. Minimum errors in speed-density relationships are found with Underwood’s exponential model, and Banks’ and Smulders’ models that assume linear flow-density. Dynamic analogues in Gazis, Herman and Rothery (GHR) form appear to reflect rational behaviour. The models are consistent with constant propagation speed of jam waves if these are dominated by start waves. Smulders’ model predicts slightly higher jam wave speed, consistent with slight convexity of the flow-density relationship.