This paper describes a set of methods for randomly drawing traces in large models either uniformly among all traces, or with a coverage criterion as target. Classical random walk methods have some drawbacks. In case of irregular topology of the underlying graph, uniform choice of the next state is far from being optimal from a coverage point of view. Moreover, for the same reason, it is generally not practicable to get an estimation of the coverage obtained after one or several random walks: it would require some complex global analysis of the model topology. We present here some methods that give up the uniform choice of the next state. These methods bias this choice according to the number of traces, or states, or transitions, reachable via each successor.