Randomly oriented single crystals of high-purity titanium were prepared by strain annealing and were subjected to multiple-step fatigue testing under strain-controlled conditions, in order to determine their cyclic stress-strain curves (CSSCs). These were found to fall into three groups, depending on orientation and the extent of slip and twinning. For those crystals oriented for single prismatic slip, a plateau was observed in the CSSCs, persistent slip bands (PSBs) occurred, and the plateau stress was 38 MPa. In a second group, oriented for prismatic slip but for which cross-slip and twinning was favored, the plateau was suppressed and the flow stresses were higher. In a third group, connected with orientations on the borders of the unit triangle, extensive hardening occurred, the CSSCs were steep, and there were multiple cases of slip and twinning. The results are interpreted in terms of maps in the stereographic projection recording the Schmid factors for the various deformation modes.