It appears to be an open question whether for every regular uncountable regular $\lambda$, every automorphism of $P(\lambda)/fin$ is trivial on a co-countable set. We will show that a small fragment of Martin's Axiom implies that if $\lambda$ is at most the continuum then every automorphism of $P(\lambda)/fin$ which is trivial on sets of cardinality less than $\lambda$ is trivial.