Channel boosting is improved in non-volatile storage to reduce program disturb. A pre-charge module voltage source is used to pre-charge bit lines during a programming operation. The pre-charge module voltage source is coupled to a substrate channel via the bit lines to boost the channel. An additional source of boosting is provided by electromagnetically coupling a voltage from a conductive element to the bit lines and the channel. To achieve this, the bit lines and the channel are allowed to float together by disconnecting the bit lines from the voltage sources. The conductive element can be a source line, power supply line or substrate body, for instance, which receives an increasing voltage during the pre-charging and is proximate to the bit lines.