The labyrinth seal with a honeycomb land is one of the most typical sealing solutions used in gas turbines. The paper presents an analysis of a straight-through seal with two fins. Such seals are used in places with limited space and where design and tribological constraints are of great importance. At a small number of the labyrinth fins, an improvement in the labyrinth performance can bring notable operating benefits. The paper presents optimisation of the seal labyrinth with different geometrical land configurations. The first part describes the labyrinth seal geometry and individual land types. The analysis covers seals with a honeycomb land, a squeezed-honeycomb land, a rhomboid land and a smooth land. The seal computational model and the optimisation task algorithm are presented. The objective function is minimization of the discharge coefficient, and the parameters are the labyrinth geometrical quantities: the fin height, the fin position, the fin thickness and the fin inclination angle. The optimisation task is solved for each land type. The results of individual optimisation tasks are presented and discussed, and the potential for improvement in the seal efficiency by means of appropriate selection of both the labyrinth parameters and the type of the land is pointed out. The obtained values of the reduction in the discharge coefficient reach 18% compared to the reference labyrinth configuration. However, taking account of both the labyrinth and the land shape, the benefit of 22.4% is achieved in comparison to the reference configuration with a honeycomb land. (C) 2018 Elsevier Ltd. All rights reserved.