  In this article we correct the proof of a uniqueness result for self-similar
solutions to Smoluchowski's coagulation equation for kernels $K=K(x,y)$ that
are homogeneous of degree zero and close to constant in the sense that
\begin{equation*}
  -\varepsilon \leq K(x,y)-2 \leq \varepsilon \left(
\Big(\frac{x}{y}\Big)^{\alpha} + \Big(\frac{y}{x}\Big)^{\alpha}\right)
\end{equation*} for $\alpha \in [0,\frac 1 2)$. Assuming in addition that $K$
has an analytic extension to $\mathbb{C}\setminus(-\infty,0]$ and prescribing
the precise asymptotic behaviour of $K$ at the origin, we prove that
self-similar solutions with given mass are unique if $\varepsilon$ is
sufficiently small.
