  The demonstration and use of nonlocality, as defined by Bell's theorem, rely
strongly on dealing with non-detection events due to losses and detector
inefficiencies. Otherwise, the so-called detection loophole could be exploited.
The only way to avoid this is to have detection efficiencies that are above a
certain threshold. We introduce the intermediate assumption of limited
detection efficiency, e.g. in each run of the experiment the overall detection
efficiency is lower bounded by $\eta_{min} > 0$. Hence, in an adversarial
scenario, the adversaries have arbitrary large but not full control over the
inefficiencies. We analyze the set of possible correlations that fulfil Limited
Detection Locality (LDL) and show that they necessarily satisfy some linear
Bell-like inequalities. We prove that quantum theory predicts violation of one
of these inequalities for all $\eta_{min} > 0$. Hence, nonlocality can be
demonstrated with arbitrarily small limited detection efficiencies. Finally we
propose a generalized scheme that uses this characterization to deal with
detection inefficiencies, which interpolates between the two usual schemes,
postselection and outcome assignment.

Quantum Physics