The early stochastic traffic assignment models (e.g. Dial, 1971) build on the assump-tion that different routes are independent (the logit-model concept). Thus, the models gave severe problems in networks with overlapping routes. Daganzo & Sheffi (1977) suggested to use probit based models to overcome this problem. Sheffi & Powell (1981) presented a practically operational solution algorithm in which the travel resistance for each road segment is adjusted according to a Monte Carlo simulation following the Normal-distribution. By this the road users’ ‘perceived travel resistances’ are simulated. A similar concept is used as a part of the Sto-chastic User Equilibrium model (SUE) suggested by Daganzo and Sheffi (1977) and operationalized by Sheffi & Powell (1982). In the paper it is discussed whether this way of modelling the ‘perceived travel resistance’ is sufficient to describe the road users actual behaviour. It is showed, that the ‘perceived travel resistance’ to a certain extent can make up for the road users lack of knowledge on the ‘true’ travel resistances. However, it is also showed that it does not fully consider varia-tions in the road users utility functions (e.g. the weighting of travel time versus travel length). A simple heuristic modification on SUE is presented which models both. To illustrate the theoretical discussions in the paper, bundles of routes between two zones in Copenhagen are presented according to the different principles and compared with results from a stop-interview survey. In addition tests of the methods on a real-size traffic model of Copenhagen (4000 links, 300 zones) are presented.