Local contact line pinning prevents droplets from rearranging to minimal global energy, and models for droplets without pinning cannot predict their shape. We show that experiments are much better described by a theory, developed herein, that does account for the constrained contact line motion, using as an example droplets on tilted plates. We map out their shapes in suitable phase spaces. For 2D droplets, the critical point of maximum tilt depends on the hysteresis range and Bond number. In 3D, it also depends on the initial width, highlighting the importance of the deposition history.