Deep desulfurization of gas oils to sulfur levels below the currently legislated 0.05 wt.% is rendered difficult by the presence of refractory species as part of a spectrum of sulfur compounds that have widely differing reactivities. This distribution of reactivities is reflected in a high apparent order (approximately 2) in total sulfur for a plug-flow reactor. The consequences of this apparent kinetic behaviour for required catalyst volumes and axial profiles of hydrogen sulfide in a reactor for deep desulfurization are examined. Hydrogen sulfide proved to strongly suppress the conversion rate of sulfur compounds, including that of the refractory alkyl substituted dibenzothiophenes crucial for deep desulfurization. A number of process configurations are discussed that avoids or reduces the problem of hydrogen sulfide inhibition. These include several variants of a two-step process in which the bulk of sulfur is removed in a first step, followed by further desulfurization down to low sulfur levels in a second step with fresh, H2S-free hydrogen gas. The theoretically most ideal option, that of operation with countercurrent flow of oil and gas, is not possible in packed beds of the usual catalyst particles because of the occurrence of flooding at industrially relevant fluid velocities. Some novel reactor concepts based on special structured packings or monoliths that allow such countercurrent operation are presented.