An assembly for positioning a well access line in a well. The assembly is located between a supply of well access line and a well, with the line running through the assembly and to the well. Multiple pulleys are incorporated into the assembly about which a well access line such as a conventional wireline may be wrapped. The pulleys are biased to one another such that slack in the line may be stored at the assembly and drawn on in the event of line tension spiking up to a predetermined amount. As such, tension in the line may be kept to a minimum so as to avoid damage to the line during a well access operation. Furthermore, should the tension in the line fail to come back down to below the predetermined amount, the well access operation may be halted in an automated manner. Halting may proceed while continuing to allow take-up of the slack in the line until completed halting of the operation is achieved.