  We present the expected performance regarding fast sky localization of
coalescing binaries with a network of three gravitational wave detectors having
heterogeneous sensitivities, such as the LIGO-Virgo network. A hierarchical
approach can be used in order to make an effective use of information from the
least sensitive detector. In this approach, the presence of an event seen in
coincidence in the two more sensitive detectors triggers a focused search in
the data of the third, less sensitive, detector with a lower signal-to-noise
ratio (SNR) threshold. We investigate the benefit for sky localization that can
be expected in such an approach, using simulated data and signals. We find that
as the sensitivity of Virgo approaches one third of the LIGO sensitivity, the
accuracy and precision of the localization can be improved by about a factor 3
when Virgo data are searched with an SNR threshold around 3.5.
