  The recent advent of chirped-pulse FTMW technology has created a plethora of
pure rotational spectra for molecules for which no vibrational information is
known. The growing number of such spectra demands a way to build empirical
potential energy surfaces for molecules, without relying on any vibrational
measurements. Using ZnO as an example, we demonstrate a powerful technique for
efficiently accomplishing this. We first measure eight new ultra-high precision
($\pm2$ kHz) pure rotational transitions in the $X$-state of ZnO. Combining
them with previous high-precision ($\pm50$ kHz) pure rotational measurements of
different transitions in the same system, we have data that spans the bottom
10\% of the well. Despite not using any vibrational information, our empirical
potentials are able to determine the size of the vibrational spacings and bond
lengths, with precisions that are more than three and two orders of magnitude
greater, respectively, than the most precise empirical values previously known,
and the most accurate \emph{ab initio} calculations in today's reach. By
calculating the $C_{6},$ $C_{8},$ and $C_{10}$ long-range constants and using
them to anchor the top of the well, our potential is \emph{globally} in
excellent agreement with \emph{ab initio} calculations, without the need for
vibrational spectra and without the need for \emph{any} data in the top 90\% of
the well.
