The present invention relates to a unit (10) for molding at least one vessel from a preform made of a thermoplastic material, comprising at least one mold (12) including at least two molding elements (14) respectively mounted in two mold holders (16) that are rotatably mounted about an axis of rotation (o) between an open position and a closed position of the unit (10) in which the molding elements (14) are joined along a parting line (P), and compensation means (30) that are controlled to apply, using a pressurized fluid, a compensation pressure for urging the molding elements (14) against one another at the parting line (P) and for hindering the pressure from a pressurized blowing fluid applied onto the molding elements (14) when molding a vessel from a preform, characterized in that the compensation means (30) control the mold holders (16) in order to clamp same against one another in the closed position of the molding unit (10) and to apply said compensation pressure.