Gas and downhole water sink-assisted gravity drainage (GDWS-AGD) is a new process of enhanced oil recovery (EOR) in oil reservoirs underlain by large bottom aquifers. The process is capital intensive as it requires the construction of dual-completed wells for oil production and water drainage and additional multiple vertical gas-injection wells. The costs could be substantially reduced by eliminating the gas-injection wells and using triple-completed multi-functional wells. These wells are dubbed triple-completion-GDWS-AGD (TC-GDWS-AGD). In this work, we design and optimize the TC-GDWS-AGD oil recovery process in a fictitious oil reservoir (Punq-S3) that emulates a real North Sea oil field. The design aims at maximum oil recovery using a minimum number of triple-completed wells with a gas-injection completion in the vertical section of the well, and two horizontal well sections—the upper section for producing oil (from above the oil/water contact) and the lower section for draining water below the oil/water contact. The three well completions are isolated with hydraulic packers and water is drained from below the oil–water contact using the electric submersible pump. Well placement is optimized using the particle swarm optimization (PSO) technique by considering only 1 or 2 TC-GDWS-AGD wells to maximize a 12-year oil recovery with a minimum volume of produced water. The best well placement was found by considering hundreds of possible well locations throughout the reservoir for the single-well and two-well scenarios. The results show 58% oil recovery and 0.28 water cut for the single-well scenario and 63.5% oil recovery and 0.45 water cut for the two-well scenario. Interestingly, the base-case scenario using two wells without the TC-GDWS-AGD process would give the smallest oil recovery of 55.5% and the largest 70% water cut. The study indicates that the TC-GDWS-AGD process could be more productive by reducing the number of wells and increasing recovery with less water production.