All the standard examples for model categories are large categories. Is it possible to have a small model category? Are there any interesting examples?

EDIT:

Since a complete small category is a preorder (proposition V.2.3 in MacLane's Categories), I'd be glad to compromise the limit axioms to be as in Quillen's original definition, demanding only finite limits and colimits. In particular, I don't consider a trivial model structure to be interesting.