Tiny mushrooms

Appearing on the surface of some used potting soil, a mix of homemade compost and commercial potting mix - tiny (about 3 cm tall) transient fungal fruiting bodies, exquisitely delicate and lasting only a few hours from opening to collapse.  Careful study of various fungus identification sites told me that this is a mushroom in form being soft and fleshy with gills under the cap, but yielded no clear idea of its name.  Anonymous but beautiful, and reminding me of a world about which I know little...  

I do know that fungi are very important to our survival - they are involved in recycling organic matter and assisting plants to get the nutrients they need from the soil, are the source of medicines like penicillin, and are used for biological pest control.  They also provide us with tasty nutritious meals, but not without some risk - there are very poisonous ones, so there is an element of adventure for those bold enough to gather them for consumption - how good is my identification?  Given what little I know, I'm sticking with eating the cultivated ones!