Processes for combining the stripping sections for two different reaction zones, such as a diesel hydrotreating zone and a naphtha hydrotreating zone. The stripping section includes an air cooler, a combined overhead receiver and two different separation sections. The two separation sections may be in the same column, but be fluidically separated. Alternatively the two sections may be in different columns. A stream from the second section may be used as a reflux from the first. While a stream from the combined overhead condenser may provide a reflux for the first section.