A low-density, high-strength concrete composition that is lightweight and self-compacting or non-self-compacting, with a low weight-fraction of aggregate to total dry raw materials, and a highly-homogenous distribution of a non-absorptive and closed-cell lightweight aggregate such as glass microspheres or copolymer polymer beads or a combination thereof, and the steps of providing the composition or components. Lightweight concretes formed therefrom have low density, high strength-to-weight ratios, and high R-value. The concrete has strength similar to that ordinarily found in structural lightweight concrete but at a lower density, such as an oven-dried density as low as 40 lbs./cu.ft. Such strength-to-density ratios range approximately from above 30 cu.ft/sq.in. to above 110 cu.ft/sq.in., with a 28-day compressive strength ranging from about 3400 to 8000 psi.