We construct short retractions of a CAT(1) space to its small convex subsets. This construction provides an alternative geometric description of an analytic tool introduced by Wilfrid Kendall.Our construction uses a tractrix flow which can be defined as a gradient flow for a family of functions of certain type. In an appendix we prove a general existence result for gradient flows of time-dependent locally Lipschitz semiconcave functions, which is of independent interest.Proof. Note that geodesics [α(t)p] lie in Dom f t for any t.Since f t is λ-concave, we haveHence the only-if part follows. Given a point p ∈ U and t, consider a pointp ∈ [α(t)p]. Applying ➎ forp and the triangle inequality, we get