Thanks for this post, which has just solved my problem, which is to set the SINGULAR value in PROC MIXED to something a bit smaller.. I tried to find this in the SAS documentation but failed. "Machine epsilon" is mentioned many times in the statistical procedures, but searching in the documentation for "machine epsilon" does not find the CONSTANT function because it is described differently there, as "Machine precision constant". The parameter is 'MACEPS', so whoever wrote the page must know. I find this deeply frustrating. Please improve the documentation.