  Several neutrino experiments have reported results that are potentially
inconsistent with our current understanding of the lepton sector. A candidate
solution to these so-called short-baseline anomalies is postulating the
existence of new, eV-scale, mostly sterile neutrinos that mix with the active
neutrinos. This hypothesis, however, is strongly disfavored once one considers
all neutrino data, especially those that constrain the disappearance of muon
and electron neutrinos at short-baselines. Here, we show that if the
sterile-active mixing parameters depend on the energy-scales that characterize
neutrino production and detection, the sterile-neutrino hypothesis may provide
a reasonable fit to all neutrino data. The reason for the improved fit is that
the stringent disappearance constraints on the different elements of the
extended neutrino mixing matrix are associated to production and detection
energy scales that are different from those that characterize the anomalous
LSND and MiniBooNE appearance data. We show, via a concrete example, that
secret interactions among the sterile neutrinos can lead to the results of
interest.
