Abstract: The paper proposes enhanced algorithms for two of the three basic steps in Low Earth Orbit (LEO) satellite network routing: the downlink routing and the inter-satellite links (ISLs) routing. In this study we refer to polar/near-polar constellations and to connectionless routing protocols such as the ones based on the Internet Protocol (IP). In particular a downlink routing procedure is proposed that does not exploit any external localization system to identify the position of the destination mobile terminal. In addition, an ISL routing algorithm is proposed that improves the one based on the minimization of the number of hops, by reducing the overall path length of the connection and, hence, the end-to-end delay. The improved algorithms are evaluated in terms of system performance and computational burden. At the price of a neglectable increase in the computational complexity, a significant improvement in the end-to-end delay is achieved by using the proposed algorithm, when the source and the destination interface are largely spaced in latitude and longitude, with a consequent benefit on the overall LEO network efficiency.