  Using an invariant modification of Jensen's "minimal $\varPi^1_2$ singleton"
forcing, we define a model of ZFC, in which, for a given $n\ge2$, there exists
a lightface $\varPi^1_n$ unordered pair of non-OD (hence, OD-indiscernible)
countable sets of reals, but there is no $\varSigma^1_n$ unordered pairs of
this kind.
