When you get fresh flowers as a gift, you can compost them after the petals have faded. Organic or conventionally grown stems can be added right to the compost heap; throw the whole bouquet right in, and it will break down into beneficial mulch. But do not pour the water in the vase on top of the compost heap. Most florists use a powdery biocide in the water to help keep it fresh by killing bacteria. This same chemical agent can be harmful to a healthy heap and can kill microbes in your compost.