Turbidite hydrocarbon reservoirs are complex features, that need to be described in detail and represented as clearly as possible. The morphology and internal distribution of elementary distributary channels are dependent on depositional settings, leading to diverse arrangements at different scales. Reservoir modelling usually requires a description of sedimentary heterogeneity on a scale smaller than that given by seismic resolution. This is because seismic data only display the outside geometry of their lateral stack, i.e. a turbidite fairway. Complexes of Laterally Offset Stacked Turbidite Channels (LOSCs) also require a description based on the scales of individual channel bodies. The most common representation of channels in a fairway is by stochastic object modelling; i.e. populating the observed fairway with realistic forms representing individual channels, but with no established consistency between the individual channels. On the other hand, one essential characteristic of LOSCs is that it evolves by progressive migration laterally and/or downdip. Stochastic object modelling provides an inadequate representation of this progressive evolution, and consequently, a poor rendering of the heterogeneity distribution in the reservoir. The method we propose consists of defining a realistic succession of individual channels that can accurately build the fairway observed on seismic. ‘Realism’ is defined using criteria from the shape of individual channels, and based on the amount of displacement necessary between successive episodes. Depending on seismic resolution, the system can be constrained by one or several positions of individual channels (the most recent position of the channel is often filled with shale, therefore visible on seismic and usable as a control point). The final result is a deterministic succession of channels laterally stacked to build the seismically observed envelope. Even with no calibration, the resulting architecture respects the general ‘texture’ of the complex and provides a better simulation of flow pathways than that achieved by random object modelling.