We present the results of global analyses of short-baseline neutrino oscillation data in 3 + 1, 3 + 2 and 3 + 1 + 1 neutrino mixing schemes. We show that the data do not allow us to abandon the simplest 3 + 1 scheme in favor of the more complex 3 + 2 and 3 + 1 + 1 schemes. We present the allowed region in the 3 + 1 parameter space, which is located at Delta m(41)(2) between 0.82 and 2.19 eV(2) at 3 sigma. The case of no oscillations is disfavored by about 6 sigma, which decreases dramatically to about 2 sigma if the Liquid Scintillating Neutrino Detector (LSND) data are not considered. Hence, new high-precision experiments are needed to check the LSND signal.