Compared with an otherwise identical option-free bond, when interest rates fall, the price of a callable bond will:
When interest rates fall, the price of the embedded call option increases. The price of a callable bond equals the price of an option-free bond minus the price of the embedded call option. So, the price of the callable bond will not increase as much as an option-free bond because the price of the call option is increasing. As interest rates fall, the bond is more likely to be called, limiting the upside price increase potential.