The present invention relates to methods of making an oil product from plant material that is used to make alcohol (e.g., ethanol) via fermentation. The methods extract oil from the plant material (e.g., corn oil from corn) before exposing to the fermented plant material to distillation temperatures so as to reduce the levels of free fatty acids and/or alcohol esters that can be generated by exposing the oil to distillation temperatures. The present invention also related to oil products made by such methods.