We discuss Euler characteristics for finitely generated modules over Iwasawa
algebras. We show that the Euler characteristic of a module is well-defined
whenever the 0th homology group is finite if and only if the relevant compact
p-adic Lie group is finite-by-nilpotent and that in this case all pseudo-null
modules have trivial Euler characteristic. We also prove some other results
relating to the triviality of Euler characteristics for pseudo-null modules.