An interbody or intervertebral spacer device for placement in an interspinous space between a pair of adjacent interspinous processes includes arcuate opposed abutment surfaces sized and shaped for engaging adjacent spinal processes. A curved through channel is disposed between the opposed abutment surfaces. A pair of bands is receivable in the curved through channel. A method of implanting such an interspinous spacer includes the steps of making an incision lateral to the spine; laterally inserting the spacer between a pair of interspinous processes without detachment of the supraspinous ligament; and laterally securing the spacer to the pair of interspinous processes with a pair of bands.