IDs - Mycena and Peziza(?)

[Acutipuerilis]

Hi All,
Any help with these two would be much appreciated... both found in a south London park.

Firstly a Peziza species, taken in March, growing out of a felled log (not sure of the tree species, but most likely either a lime or horse chestnut). Roughly 25 mm diameter, and I can't pin it down to anything.



Secondly, a Mycena from a couple of days ago, growing out of woody debris, with 2-3 mm diameter caps. It looks to me a bit like M. rorida, but I'm really guessing with these things.




Many thanks,
Joe

[Fungus Ken]

The first cup fungus is a very neat cup, unlike some Pezizas. Could it be a Tarzetta?

The Mycena is probably Mycena speirea.

Ken

[Acutipuerilis]

Thank you Ken - will look into it, but I think you're right on Tarzetta! (And of course the Mycena as well, which I tend to have difficulty with... )