We study in numerical experiments in plane Couette flow the possibility to follow a turbulent state created at higher Reynolds numbers down to lower ones. For annealing rates faster than the escape time but slower than the relaxation rate to the turbulent state turbulence persisted for some time down to Reynolds numbers around 240. This is less than the accepted value for the transition to turbulence (about 320) but still larger than the lowest bifurcation point for stationary states (about 125).