  In this paper we study factorising twists of the massless AdS_3 and AdS_2
integrable R-matrices, and explore the programme of analysis of form factors
which Maillet et al developed for ordinary spin-chains. We derive the
factorising twists from the universal R-matrix of the gl(1|1) Yangian double,
and discuss the RTT relations for the two- and three-site monodromy matrix. We
show how the twist can be used to compute a simple scalar product. We then
implement our construction in the language of free fermions. Finally, we show
how to obtain the massless AdS_2 quantum R-matrix from the Yangian universal
R-matrix, and compute a peculiar factorising twist for this case as well.
