A survey for NEO aiming at 90% completeness for a given size range cannot ignore that a significant fraction of the population is observable essentially only at low solar elongation, in the so called “sweet spots” There are several penalties for such low elongation: poorer observing conditions imply a lower limiting magnitude, shorter available time in each night and a more difficult orbit determination. Our aim is to show that these difficulties can be overcome. We have tested the observation procedures and the mathematical methods of orbit determination on two sweet spot test runs. One was performed at ESO La Silla in Jan–Feb 2005, the other at Mauna Kea in Sept–Dec 2005. The results of the tests are presented in this paper; the observed area was not large enough (especially at Mauna Kea) to discover a significant number of new NEO, the purpose was rather to identify the problems. These tests have allowed us to identify all the key elements to be accounted for in the strategy for a successful sweet spot NEO survey. When very short arc observations from different nights have to be identified, a specific difficulty occurs at the sweet spots: the same set of observations from three nights can be fitted to two incompatible orbits, in most cases including one NEO and one MBA. This can lead to two different failures (false positive, false negative) in deciding whether a NEO has been discovered. The classical theory of preliminary orbits shows that three observations at an elongation less than 116.5° can be compatible with two different orbits. From this theory we have derived an algorithm to find the alternate solution, if it exists, when only one is available. In this way we have generated a set of examples of possible discoveries with two well determined but incompatible solutions. Most of the MBA-NEO alternatives have been solved by finding a known MBA which could be identified; in two cases the MBA solution has been confirmed by a later observation.