Abstract The static user-equilibrium (UE) traffic assignment model is widely used in practice. One main computational challenge in this model is to obtain sufficiently precise solutions suitable for scenario comparisons, as quickly as possible. An additional computational challenge stems from the need in practice to perform analyses based on route flows, which are not uniquely determined by the UE condition. Past research focused mainly on the first aspect. The purpose of this paper is to describe an algorithm that addresses both issues. The traffic assignment by paired alternative segments (TAPAS) algorithm, focuses on pairs of alternative segments as the key building block to the UE solution. A condition of proportionality, which is practically equivalent to entropy maximization, is used to choose one stable route flow solution. Numerical results for five publicly available networks, including two large-scale realistic networks, show that the algorithm can identify highly precise solutions that maintain proportionality in relatively short computation times.