SWIFT J1756.9-2508 is one of the few accreting millisecond pulsars (AMPs) discovered to date. We report here the results of our analysis of its aperiodic X-ray variability, as measured with the Rossi X-Ray Timing Explorer during the 2007 outburst of the source. We detect strong (~35%) flat-topped broadband noise throughout the outburst with low characteristic frequencies (~0.1 Hz). This makes SWIFT J1756.9-2508 similar to the rest of AMPs and to other low-luminosity accreting neutron stars when they are in their hard states, and enables us to classify this AMP as an atoll source in the extreme island state. We also find a hard tail in its energy spectrum extending up to 100 keV, fully consistent with such source and state classification.