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.