Estimate entropy, based upon observed frequency counts
Like most things of this nature the best method is best found by empirical evaluation. One thing worth noting is that most smoothing schemes can be thought of as the incorporation of a prior into your likelihood estimate. For example if you are trying to estimate the parameter $\theta$ of a binary random variable $X$ and you have data $\mathcal{D} = \{x_1, \ldots, x_n\}$ consisting of i.i.d. realizations of $X$ then your posterior takes the form

$$
\begin{align*}
P(\theta|\mathcal{D}) 
&amp;\varpropto P(\theta)P(\mathcal{D}|\theta)\\
\end{align*}
$$
Assuming $P(\theta) = B(\alpha,\beta)^{-1}\theta^{\alpha-1}(1-\theta)^{\beta-1}$, i.e., a Beta distribution and letting $n_1 = |\{x_i \in \mathcal{D} \colon x_i = 1\}|$ then we have

$$
\begin{align*}
P(\theta|\mathcal{D})
&amp;\varpropto  \theta^{\alpha-1}(1-\theta)^{\beta-1} \theta^{n_1}(1-\theta)^{n - n_1}\\
&amp;= \theta^{n_1 + \alpha - 1}(1- \theta)^{n - n_1 + \beta - 1}.
\end{align*}
$$
Notice the effect of the hyperparameters ($\alpha$ and $\beta$) is essentially to just add some constant to your counts of each possible outcome. So additive smoothing (at least all applications I've encountered) is really just a special case of Bayesian estimation.