We used to believe that deeper water was better. What is actually true is that 2 – 3 inches of water is suitable for most flowers 12 – 18 inches long. The longer the flower the further the distance from the water source to the flower. However, never drown flowers or place them in water that is deeper than they are. Getting water on or in the bloom of the flower can cause bacteria (botrytis, a brown slimy fungus) to appear on the flower and kill the flower.
Always remove any and all leaf or foliage material that will fall below the water line. This will prevent bacteria from growing in the water. Bacteria in the water are the #1 enemy of fresh flowers. No bacteria = fresher (longer lasting) flowers!