  Quantum imaging can beat classical resolution limits, imposed by diffraction
of light. In particular, it is known that one can reduce the image blurring and
increase the achievable resolution by illuminating an object by entangled light
and measuring coincidences of photons. If an $n$-photon entangled state is used
and the $n$th-order correlation function is measured, the point-spread function
(PSF) effectively becomes $\sqrt n$ times narrower relatively to classical
coherent imaging. Quite surprisingly, measuring $n$-photon correlations is not
the best choice if an $n$-photon entangled state is available. We show that for
measuring $(n-1)$-photon coincidences (thus, ignoring one of the available
photons), PSF can be made even narrower. This observation paves a way for a
strong conditional resolution enhancement by registering one of the photons
outside the imaging area. We analyze the conditions necessary for the
resolution increase and propose a practical scheme, suitable for observation
and exploitation of the effect.
