The present application and the resultant patent provide improved gas turbine component sealing. In one example embodiment, a gas turbine segment seal assembly may include a first tapered segment seal with a first tapered portion having a first tapered surface and a first taper angle. The gas turbine segment seal assembly may include a second tapered segment seal with a second tapered portion having a second tapered surface and a second taper angle. The gas turbine segment seal assembly may include a seal pin positioned in between the first tapered segment seal and the second segment seal and adjacent to the first tapered surface and the second tapered surface.