In the design of an aerobic fed-batch process to produce, for example, a pharmaceutical protein, the volumetric production rate will eventually become limited by mass transfer when the biomass concentration exceeds a certain upper limit x*. It appears to be common practice to switch from exponential feed of substrate to a constant feed rate when x* is reached. This is done to avoid oxygen starvation with a potential risk of undesired stress responses. But with a constant feed rate the carbon source (glucose) concentration may decrease to a low level with a resulting loss of viability and an undesired production of endotoxins. It is shown that an exponential feeding strategy may be continued, but with a smaller exponent than the one used before oxygen limitation occurs. This will diminish the potential detrimental effects on the culture due to low glucose concentration, and the total time to reach a given final biomass concentration will be reduced.