Disclosed are several examples of an apparatus for connecting the free ends of two electrical power transmission lines having conductor strands disposed around a central, reinforcing core. The examples include an inner sleeve having a body defining an inner bore passing through an axially-extending, central axis, an outer rim surface disposed radially outward from the central bore, and one or more axially-extending grooves penetrating the body at the outer rim surface. Also included is an outer splice having a tubular shaped body with a bore passing coaxially through the central axis, the bore defining an inner rim surface for accepting the inner sleeve. The inner bore of the inner sleeve accepts the reinforcement cores of the two conductors, and the grooves accept the conductor strands in an overlapping configuration so that a majority of the electrical current flows between the overlapped conductor strands when the conductors are transmitting electrical current.