  We explore the sensitivity and completeness of long baseline interferometric
observations for detecting unknown, faint companions around bright unresolved
stars. We derive a linear expression for the closure phase signature of a faint
companion in the high contrast regime (<0.1), and provide a quantitative
estimation of the detection efficiency for the currently offered four-telescope
configurations at the Very Large Telescope Interferometer. The results are
compared to the performances provided by linear and Y-shaped interferometric
configurations in order to identify the ideal array. We find that all
configurations have a similar efficiency in discovering companions wider than
10mas. Assuming a closure phase accuracy of 0.25deg, that is typical of
state-of-the-art instruments, we predict a median dynamic range of up to six
magnitudes when stacking observations obtained at five different hour angles.
Surveying bright stars to search for faint companions can be considered as an
ideal filler programme for modern interferometric facilities because that
places few constraints on the choice of the interferometric configuration.
