What can be done to reduce/eliminate snoring, without using a mask at night?

Multiple. Lose weight, avoid alcohol, don't sleep on your back (fill a sock with tennis balls, and sew it to the back of a t shirt) use a humidifier, can try a mouthpiece that helps reposition the jaw (see your dentist).
Sleep apnea. Several possibilities: some people only snore if they sleep on their back, so try avoiding that. Losing weight. See an ear nose & throat specialist to evaluate your tonsils, adenoids and sinus wear a custom made dental device that holds your jaw forward while you sleep thereby increasing the airway.
Relieve the Blockage. Anything that relieves the airway blockage will lessen the snoring. Snoring equals a blocked airway. Nasal sprays, weight loss, sleeping with head elevated, nasal surgery, palate surgery or implants, and snoring mouthpieces may be helpful also.