After this, we have a sliding scale of priority. First and most important are those NEOs that currently have a chance of better than 1 in a billion of hitting the Earth sometime in the next 100 years. Next, we target NEOs needing further observations as identified by the Spaceguard Central Node (SCN). At the same priority we place Potentially Hazardous Objects (PHOs) where further observations would significantly improve their orbits. A PHO is a NEO that can come within 7.5 million kilometers of Earth, and is probably 150m across or larger, which would mean that it would probably hit the ground if it entered our atmosphere. Finally, we target any other NEOs where further observations would significantly improve the orbit. Often these are NEOs discovered more than a year ago, but which haven't been seen for months or even years.
All of this assumes a dark sky (no moon), no clouds and good seeing i.e. the atmosphere is not very turbulent. Hence when we decide what to observe we also have to fold in where the moon is in the sky (easy!), and what the likely weather will be (hard!). So don't be surprised if we observe brighter NEOs with small positional unceratinties - in moonlight with high cirrus clouds in the sky, they may be all we can see!