In bedload transport modelling, it is usually presumed that transported material is fed by the bed itself. This may not be true in some mountain streams where the bed can be very coarse and immobile for the majority of common floods, whereas a finer material, supplied by bed-external sources, is efficiently transported during floods, with marginal morphological activities. This transport mode was introduced in an earlier paper as ‘travelling bedload’. It could be considered an extension of the washload concept of suspension, applied to bedload transport in high-energy, heavily armoured streams. Since this fine material is poorly represented in the bed surface, standard surface-based approaches are likely to strongly underestimate the true transport in such streams. This paper proposes a simple method to account for travelling bedload in bedload transport estimations. The method is tested on published datasets and on a typical Alpine stream, the Roize (Voreppe, France). The results, particularly on active streams that experience greater transport than expected from the grain sizes of their bed material, reinforce the necessity of accounting for the ‘travelling bedload concept’ in bedload computation. The method relevance is discussed regarding varying flood magnitudes, geomorphic responses and eventual anthropic origin of the ‘travelling bedload’ phenomena. To conclude, this paper considers how to compute bedload transport for a wide range of situations, ranging from sediment-starved cases to the general mobile bed alluvial case, including the intermediate situation of external source supply on armoured bed.