  We discuss oscillations of atmospheric and solar neutrinos into sterile
neutrinos in the 2+2 scheme. A zeroth order sum rule requires equal
probabilities for oscillation into nu_s and nu_tau in the solar+atmospheric
data sample. Data does not favor this claim. Here we use scatter plots to
assess corrections of the zeroth order sum rule when (i) the 4 x 4 neutrino
mixing matrix assumes its full range of allowed values, and (ii) matter effects
are included. We also introduce a related "product rule". We find that the sum
rule is significantly relaxed, due to both the inclusion of the small mixing
angles (which provide a short-baseline contribution) and to matter effects. The
product rule is also dramatically altered. The observed relaxation of the sum
rule weakens the case against the 2+2 model and the sterile neutrino. To
invalidate the 2+2 model, a global fit to data with the small mixing angles
included seems to be required.
