We show that any bounded integral function $f : A \times B \mapsto \{0,1, \dots, Δ\}$ with rank $r$ has deterministic communication complexity $Δ^{O(Δ)} \cdot \sqrt{r} \cdot \log r$, where the rank of $f$ is defined to be the rank of the $A \times B$ matrix whose entries are the function values. As a corollary, we show that any $n$-dimensional polytope that admits a slack matrix with entries from $\{0,1,\dots,Δ\}$ has extension complexity at most $\exp(Δ^{O(Δ)} \cdot \sqrt{n} \cdot \log n)$.