This invention provides a method for reducing the water saturation in the near-well region. Along with various well treatment possibilities, one application of this invention increases the injectivity rate of a substantially nonaqueous fluid into a subterranean formation. The preferred embodiment uses this invention to increase the injectivity of solvent gas into an oil-bearing formation for enhancing the amount and/or rate of oil recovery from the formation. The method includes injecting a second fluid into the near-well region of the injection well to displace at least a portion of the water from that region. Displacement of the water and subsequent displacement of the secondary fluid allow maximum injectivity for the primary solvent being injected for oil recovery.