A concrete comprises in relative parts by weight: 100 of Portland cement; 0.25 to 9 of a defoamer; 0.001 to 6 of a surfactant; 0 to 230 of coarse gravel and/or fine gravel and/or shear enhancers; 0 to 85 of sand; 0 to 60 of a particulate pozzolanic or non-pozzolanic material or a mixture thereof having a mean particle size less than 15 micrometers; 0 to 80 of a particulate pozzolanic or non-pozzolanic material or a mixture thereof having a mean particle size between 15 to 88 micrometers; 0.3 to 18 of a water-reducing superplasticizer; 0 to 14 of polyethylene fibers; and 5 to 40 of water. An air mixing process using a tightly sealed mixing tool is used to thoroughly mix the constituents of the concrete before adding the water for curing. By adjusting relative parts in the composition, concretes of high and ultrahigh performance can be achieved efficiently.