A non-drip, preferably self-adhesive, silicone elastomer composition crosslinkable by polyaddition, such as those polyorganosilanes (POS) bearing C2═C6≡Si-alkenyl units and ≡Si—H units but excluding fluorinated POS. The composition includes at least a thixotropic additive containing at least a fluorinated resin, preferably based on polyfluoroethylene (PTFE). The composition may be prepared from a Si—Vi polydimethylsiloxane (PDMS) and a Si—H PDMS crosslinked by platinum catalysis. Polytetrafluorethylene, a filler, particularly one containing silicone, optionally a ternary adherence promoter such as vinyltrimethosilane/glycidoxypropyltrimethoxysilane/butyl orthotitanate, and other typical additives may be added to the composition. The composition (not excluding the fluorinated POS as a possible constituent in the composition) may be used to produce joints in situ and/or as an adhesive, particularly in upholstery.