Early studies of slurry pipeline systems were based on moderate volumetric concentrations of solids (say up to 18%), for which the excess pressure gradient caused by solids is proportional to concentration. Much larger concentrations now coming into common use show more complicated behaviour. An algebraic analysis is developed to determine desirable operating, points and associated energy consumption for settling slurries. This deals initially with the simple proportional behaviour, and then is extended to other cases. Comparison is made to recent experiments using highly concentrated settling slurries with various particle gradings. It is found that near-uniform gradings tend to have high frictional losses, while very broad gradings can give rise to energy-efficient transport at high concentrations,