using sort command

[R Kimber]

I'm trying to sort a text file of the form:
john smith, something, something

Basically, I want to sort on the surname and then on the first name, so
that all the Smiths (e.g.) end up in order of their first name.

The man page doesn't seem to explain this. Googling suggests that

sort -k2 -k1 <filename>

ought to work, but it just seems to sort on the surname.

I'd be grateful for pointers on how to do this.
- Richard.
-- 
Richard Kimber
Political Science Resources: UK General Election 2010
http://www.PoliticsResources.net/area/uk/ge10/ge10.php