A spinal implant helps stabilize vertebrae for fusion. The implant is particularly adapted for percutaneous implantation, but may also be used with other access techniques. The implant includes first and second plates that extend through a slot in a frame. When installed, the frame extends laterally through the interspinous space, and the plates extend superiorly-inferiorly along respective lateral sides of the spinous processes. The plates are moved toward one another and relative to the slot to clamp the implant to the spinous processes. The slot may be variably sized along its length, and the plates may move into differently sized portions of the slot during the clamping process.