To achieve a very similar goal I generally use the following:
\begin{frame}
\frametitle{Size changed}
\scalebox{0.8}{\begin{minipage}{1.20\textwidth}
... your content here ...
\end{minipage}}
\end{frame}
I do not know how to compute the combined values of the scale factor and of the minipage width, I generally try several values until it satisfies me.
For example, the following content:
\begin{itemize}
\item First item.
\begin{itemize}
\item First subitem.
\begin{itemize}
\item \lipsum[75]
\item \lipsum[66]
\item \lipsum[75]
\end{itemize}
\item Second subitem.
\end{itemize}
\item Second item.
\item Third item.
\end{itemize}
gives:

and if you change the scale/minipage values to 0.6/1.6 you obtain:
