  We investigate self-contracted curves, arising as (discrete or continuous
time) gradient curves of quasi-convex functions, and their rectifiability
(finiteness of the lengths) in Euclidean spaces, Hadamard manifolds and
CAT(0)-spaces. In the Hadamard case, we give a quantitative refinement of the
original proof of the rectifiability of bounded self-contracted curves (in
general Riemannian manifolds) by Daniilidis et al. Our argument leads us to a
generalization to CAT(0)-spaces satisfying several uniform estimates on their
local structures. Upon these conditions, we show the rectifiability of bounded
self-contracted curves in trees, books and CAT(0)-simplicial complexes.
