  We show that if $A$ is a subset of a group of prime order $p$ such that
$|2A|<2.7652|A|$ and $|A|<1.25\cdot10^{-6}p$, then $A$ is contained in an
arithmetic progression with at most $|2A|-|A|+1$ terms, and $2A$ contains an
arithmetic progression with the same difference and at least $2|A|-1$ terms.
This improves a number of previously known results.
