Pinwheel Marasmius, Marasmius rotula, is a tiny mushroom: the cap is less than 1.5 cm across, and the stem is less than a millimeter wide, though a couple guide books list it as 1-2 mm wide. The gills are well spaced. The cap is white or cream, pleated, and convex with a central depression with a dark spot in the center.
Kuo says that this species is nearly identical to M. capillaris, but that grows on fallen leaves rather than wood as M. rotula does. These seem to appear overnight after a rain. In truth, they were already there, just shrivelled into invisibility, but rain restores their bodies--this is a characteristic of the Marasmius genus.
Update: I studied some more of these on July 27. All the specimens I looked at had stems less than a millimeter wide. Some were as thin as .3 mm.