Wall construction block combination for a wall construction system

A wall construction block combination, comprising

• a block comprising a front surface, a back surface, a top surface, a bottom surface, and a plurality of webs extending between the front surface and the back surface to define at least two voids, each with a void perimeter, wherein at least one of the voids is at least partially bounded by a ledge within the void and along the void perimeter of at least one of the two voids;
• and
• structures on the top and bottom surfaces defining at least one protrusion at one of the top surface and the bottom surface and a recess at the other of the top surface and the bottom surface wherein the protrusion and recess are dimensioned to have an interfitting relationship with corresponding protrusions and recesses of substantially identical blocks;
• and
• an insert separate from the block and disposed on the ledge, the insert having a surface area dimensioned to have a portion of its perimeter supported by the ledge.