Coreless rolls of tissue, such as rolls of bath tissue or paper towels, are produced by winding tissue logs on a mandrel having retractable pins. During winding, the pins extend and penetrate the first several windings of the log as it is initially wound, which prevents slippage. After the winding is complete, the pins retract to allow the tissue log to slide off of the mandrel for subsequent slitting into individual product rolls and packaging. The penetration of the pins into the first several windings of the log tends to mechanically entangle and structurally unify those windings to create a “soft core”. At the same time, the properties of the tissue sheets within the soft core are the same as the other sheets within the roll and are therefore usable by the consumer.