For planar (x is an element of R-2) control systems x'= f(x, mu) with a two-valued control mu is an element of {mu(1), mu(2)} we consider small cycles created by rapidly switching between the two control values. A two-cycle is a periodic cycle on which the periodic control changes value twice in one period. Stasis is a relaxed (i.e., probabilistic) control mu(r) with a fixed point (called a stasis point) x(r) where 0=f(x(r), mu(r))=integral f(x(r), mu) d mu(r). Generically, stasis points can be approximated by two-cycles, and every two-cycle must contain a stasis point. Also generically, stasis points form curves (called stasis curves). The unit metric on these curves parameterize families of small two-cycles near the stasis curve. Under general conditions, we show that average performance is differentiable with respect to this parameterization, and thus necessary conditions for optimality of small two-cycles versus stasis can be explicitly calculated.