LEO constellations create a network that includes the satellites (as routing nodes) connected by Inter-Satellite Links, and the satellite terminals dynamically connected to one or more satellites. The combination of transient, high-rate changes with high latency presents a unique challenge for designing a routing protocol that can provide guaranteed bandwidth, and support the frequent changes without packet drops. Current works focus on end-to-end routing between multiple gateways and terminals and do not provide guaranteed service.This paper addresses the problem of routing traffic from a source terminal to a destination terminal on a LEO constellation using Asymmetric Differential Routing (ADR) to plan 'semi-fixed' routes. ADR keeps most of the planned route fixed and only minor (differential) adjustments are required to account for handovers.