The present invention relates to a locking sleeve assembly for use in a posterior spinal system including components designed to be affixed to the spinal column of a person to correct for various lateral and sagittal deformities. The locking sleeve assembly is for interconnecting an elongated rod with another structure. The locking sleeve assembly includes an elongated sleeve having a bore therethrough. The sleeve has a tapered first end and a second end having a lock member thereon. The sleeve includes at least one split extending into the sleeve. The bore is sized to slidably receive the rod. The tapered surface of the sleeve is insertable into a tapered passage of the other structure with the rod in the bore, to form an interference fit between the two tapered surfaces. The locking sleeve assemblies are used in conjunction with the spinal system which also includes a pair of smooth surfaced rods mounted in spaced relation to one another on the spinal column in conjunction with various fixation devices such as clamps with hook bodies, hooks, screws with hook bodies, and couplers. Each such fixation device utilizes locking sleeve assemblies at each connection point to secure the respective fixation device to the respective rod or rods. The coupler assemblies are provided to maintain the spacing of the rods. The method of performing surgery using the posterior spinal system is also disclosed.