The differences between simplicity of a von Neumann regular ring and simplicity of its ordered Grothendieck group K0 are investigated. In particular, we construct examples of stably finite regular rings which are not simple but have simple K0. All the nontrivial factor rings of these examples are directly infinite. Also, we prove that a simple regular ring satisfies weak comparability if and only if its category of finitely generated projective modules is strictly unperforated. © 1995 Academic Press. All rights reserved.