Mixtures of coherent and thermal fields

When I started my PhD, there arose the need to describe mixtures of coherent and thermal states, specifically the diagonal elements $p(n)$ of the density matrix (or probability to have $n$ particles) and the postdoc there came up with something that looked hideous to me: $p_{\mathrm{coh}}(n)+p_{\mathrm{th}}(n)$ (normalized).