Fast-rotating asteroids (FRAs) are considered to be small bodies having a rotation period (P) faster than the spin barrier of about 2.3 h, starting at diameters of less than 300 m. We selected the 20 fastest Arecibo radar-observed targets, with P<0.13 h (∼8 min). Some key measurements and calculations obtained from radar observations include: the Doppler bandwidth, the circular polarization ratio, radar astrometry, and (with enough signal-to-noise ratio) delay-Doppler images of the object. Rotation period data available from the Light Curve Database for the selected objects combined with the radar observations allow us to constrain the possible diameters and confirm the periods. Of the objects in this sample, the median absolute magnitude (H) is 24.9, and the median calculated diameter is 32 meters. The apparent rotation period indicated by the bandwidth can appear slower than the object’s true rotation, but not faster, providing an upper limit to the true rotation period. Asteroid cohesion required to prevent rotational disruption depends on rotation rate, density, and diameter; we performed calculations for the minimum values for cohesion via the Drucker–Prager (D–P) cohesion criterion. Most of these objects need a few to a few hundred pascals of cohesion; however four cases stand out: 2014 TV, 2015 RF36, 2015 GS2 and 2017 EK, needing a minimum cohesion on the order of a few kilopascals. These are comparable to very weak Earth rocks, and are larger than previously reported values for NEAs. •Analysis of fastest-rotating near-Earth asteroids observed from Arecibo Observatory.•Comparing radar- and lightcurve-derived rotation period, diameter, and cohesion.•We show the orbit determination for small NEAs is significantly improved when radar observations are available.•A few objects need cohesion on the order of a few kilopascals to prevent disruption.