We study the potential of a Neutrino Factory in constraining the parameter space of a scheme with one sterile neutrino separated from three active ones by an O(1) eV² mass-squared difference. We present approximated analytic expressions for the oscillation probabilities, showing that the greatest sensitivity to sterile neutrinos at a Neutrino Factory can be achieved using the ν_μ → ν_μ and the ν_μ → ν_τ oscillations. We have studied two setups: a Neutrino Factory with 50 GeV (20 GeV) stored muons, with two detectors of the Hybrid-MIND type (a magnetized ECC next to a magnetized iron calorimeter), located at L = 3000, 7500 km (L = 4000, 7500 km) from the source. Four channels have been used: ν_e → ν_μ,ν_τ; ν_μ → ν_μ,ν_τ. The relevant backgrounds, efficiencies and systematic errors have been taken into account, and we have discussed dependence of the sensitivities on the systematic errors. We have found that the 50 GeV (20 GeV) setup can constrain sin² 2θ^(4fam)₁₃ ≤ 7 × 10⁻⁵ (2 × 10⁻⁴); θ₃₄ ≤ 12° (14°); and θ₂₄ ≤ 7.5° (8°). Our results hold for any value of Δm²_SBL0.1 eV². Eventually we have shown that, if a positive signal is found, the proposed setup is able to measure simultaneously θ₃₄ and δ₃ with a precision of few degrees and few tens of degrees, respectively, solving the so-called "intrinsic" and "sign degeneracies". Combination of ν_μ disappearance and of the ν_μ → ν_τ channel, that will be called "the discovery channel'', at the two baselines is able to measure at 99% CL a new CP-violating phase δ₃ for sin² 2θ₃₄ ≥ 0.06.