We use the TOUGH+HYDRATE code to assess the production potential of some particularly challenging hydrate deposits, i.e., deposits that are characterized by any combination of the following factors: absence of confining boundaries, high thermodynamic stability, low temperatures, low formation permeability. Using high-resolution grids, we show that a new horizontal well design using thermal stimulation coupled with mild depressurization yields production rates that appear modest and insufficient for commercially viable production levels. The use of parallel horizontal wells (with the lower one providing thermal stimulation through heat addition, direct injection or circulation of warm water, and the upper one producing under a mild depressurization regime) offers tantalizing possibilities, and has the potential of allowing commercial production from a very large number of hydrate deposits that are not currently considered as production candidates if the problem of the corresponding large water production can be solved.