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This letter proposes an IP-based finely-distributed routing scheme based on two-phase routing (TPR) over shortest paths for the hose model. It is called the fine-TPR (F-TPR) scheme. Compared to the original TPR, F-TPR distributes traffic from a source node to intermediate nodes more finely, where the distribution ratio is determined for each source-destination pair. To determine an optimum set of the distribution ratios, we successfully formulate our problem as a quadratic constraint programming (QCP) formulation that can be solved by using a mathematical programming solver. Numerical results show that F-TPR greatly outperforms TPR and its performance approaches that provided by the sophisticated traffic engineering (TE) scheme of multi-protocol label switching (MPLS-TE).