The sealing device (1) for a piston (2) of which the fixed skirt (5) moves in a cylinder (8) includes a sliding skirt (6) traversed axially by a pressure transmission channel (10) and connected to the fixed skirt (5) by a mechanical inter-skirt connection (7) whilst an extensible continuous segment (9) is interposed in a sealed manner between the skirts (5, 6) and can come into contact with the cylinder (8) when its internal cylindrical segment face (12) is subjected to the pressure of a fluid (36) via the pressure transmission channel (10), a sliding skirt spring (16) tending to bring the skirts (5, 6) closer and to axially compress the extensible continuous segment (9) between the skirts (5, 6).