The fine two-phase routing (F-TPR) scheme, an IP finely-distributed load-balanced routing scheme based on two-phase routing over shortest paths, was previously presented to improve routing performances. F-TPR distributes traffic from a source node to intermediate nodes simply by using IP tunnels. F-TPR provides comparable routing performance to the sophisticated traffic engineering (TE) scheme of Multi-Protocol Label Switching (MPLS-TE). However, in practice, most routers will not be able to handle the complexity of determining and implementing uneven traffic distributions with any form of precision. This paper investigates non-split F-TPR, where traffic from a source node to a destination node is not split over multiple routes, in other words, it goes via only one intermediate node to the destination node. The problem solved by non-split F-TPR is formulated as an integer linear programming (ILP) problem. Since it is difficult to solve the ILP problem within a practical time, this paper introduces two heuristic algorithms against the ILP problem. We compare non-split F-TPR against split F-TPR and MPLS-TE. Numerical results show that non-split F-TPR matches the routing performance of F-TPR and MPLS-TE with an error of 1%, when network size is enough large.