In order to develop a more set of constraints for theories of solar wind high-speed streams a detailed study was made of the fastest streams observed at 1 AU during the time period spanning March 1971 through July 1974. Streams were accepted for study only if (1) the maximum speed exceeded 650 km s-1; (2) effects of stream-stream dynamical interaction on the flow parameters could be safely separated from the intrinsic characteristics of the high-speed regions; (3) the full width at half maximum (FWHM) of the stream when mapped back to 20 solar radii by using a constant speed approximation was greater than 45¿ in Carrington longitude; and (4) there were no obvious solar-activity-induced contaminating effects. Nineteen streams during this time interval satisfied these criteria. Average parameters at 1 AU for those portions of these streams above V=650 km s-1 were as follows: (1) the maximum speed and FWHM were 741¿49 km s-1 and 89¿¿34¿, respectively; (2) proton and electron temperatures were (2.3¿0.9) ¿105 K and (0.99¿0.08) ¿105 K, respectively; (3) the convected proton enthalpy flux of (24¿5) ¿10-3 erg cm-2 s-1 was nearly an order of magnitude larger than the radial component of conducted electron heat flux of (2.8¿0.9) ¿10-3 erg cm-2 s-1 and a factor of 2 greater than the inferred convected Alfv¿n wave energy flux of (11.6¿4.7) ¿10-3 erg cm-2 s-1 and a factor of 2 greater than the inferred convected Alfv¿n wave energy flux of (11.6¿4.7) ¿10-3 erg cm-2 s-1; (4) the proton particle flux was NV= (3.3¿0.5) ¿108 cm-2 s-1; and (5) the convected energy flux, including the flux of work done against the sun's gravitational field in traveling from the sun's surface to 1 AU, was 2.4¿0.4 ergs cm-2. Not only is it not presently known why the electrons are significantly cooler than the protons within high-speed regions, but also observed particle fluxes and convected energy fluxes for speed greater than 650 km s-1 are substantially larger than those values predicted by any of the existing theories of solar wind high-speed streams. More work is therefore needed in refining present solar wind models to see whether suitable modifications and/or combinations of existing theories based on reasonable coronal conditions can accommodate the above high-speed flow parameters.