Let $A$ be a finite set of integers such that the $2$-fold sumset $2A$ is “small”, i.e., $|2A|<c|A|$ for some constant $c$. There exists an $n$-dimensional arithmetic progression of length $c^{{\prime}}|A|$ that contains $A$, and such that $c^{{\prime}}$ and $n$ are functions of $c$ only.