Saline waters having high osmotic pressure are unsuitable for reverse osmosis desalination. Direct contact membrane distillation (DCMD) can desalt such waters provided the membrane technique is highly resistant to fouling by scaling salts. In DCMD, we had shown earlier that a rectangular cross-flow hollow fiber membrane (HFM) configuration with a specific plasma-polymerized nearly superhydrophobic coating on the membrane ensured no precipitation-based fouling from CaCO3 and CaSO4 for salt concentrations up to 19 wt %. A novel aspect of this method, oscillation of unrestrained HFMs, is illustrated here. Earlier models simulating desalination performance of such devices assumed membrane mass transfer coefficient, k(m), as an adjustable parameter for large hollow fiber modules. Here km was predicted from a recent model without any adjustable parameters, resulting in a better module water vapor flux prediction. To improve membrane module performance and productivity, simulations were carried out by varying hollow fiber ID, HFM length, and the distillate flow rate. The simulation results will help design optimum HFM modules for DCMD-based desalination.