  New neutrino degrees of freedom allow for more sources of CP-invariance
violation (CPV). We explore the requirements for accessing CP-odd mixing
parameters in the so-called 3+1 scenario, where one assumes the existence of
one extra, mostly sterile neutrino degree of freedom, heavier than the other
three mass eigenstates. As a first step, we concentrate on the nu_e to nu_mu
appearance channel in a hypothetical, upgraded version of the nuSTORM proposal.
We establish that the optimal baseline for CPV studies depends strongly on the
value of Delta m^2_14 -- the new mass-squared difference -- and that the
ability to observe CPV depends significantly on whether the experiment is
performed at the optimal baseline. Even at the optimal baseline, it is very
challenging to see CPV in 3+1 scenarios if one considers only one appearance
channel. Full exploration of CPV in short-baseline experiments will require
precision measurements of tau-appearance, a challenge significantly beyond what
is currently being explored by the experimental neutrino community.
