We study various complexity properties of suffix-free regular languages. A sequence (Lk,Lk+1,…) of regular languages in some class, where n is the quotient complexity of Ln, is most complex if its languages Ln meet the complexity upper bounds for all basic measures. It is known that there exist such most complex sequences in several classes of regular languages. In contrast to this, we prove that there does not exist a most complex sequence in the class of suffix-free regular languages. However, we do exhibit two such sequences that together meet upper bounds for all basic measures.