Described are methods of distributing a viscosity reducing solvent to a set of wells terminating in an underground oil reservoir where the variation in the net solvent injection rate is minimized. The net solvent injection rate is the difference between the total solvent injection rate and the total solvent production rate from the set of wells, for example on an instantaneous or daily rate basis. Minimizing this variation can reduce costs associated with surface solvent storage, subsurface solvent storage, and solvent supply, since solvent supply often is least expensive when supplied at near a fixed rate. One option is to operate well pairs and to inject solvent into one well of the pair while producing oil and solvent from the other well of the pair. These methods are particularly useful in solvent-dominated, cyclic or non-cyclic, viscous oil recovery processes.