A hybrid method for processing papermaking fibers to remove high density stickies typically includes utilizing a multistage array of forward cleaners coupled with a flotation cell which increases overall efficiency of the system. In a preferred embodiment, a first rejects aqueous stream from a first stage bank of centrifugal cleaners is treated in a flotation cell before being fed to a second stage bank of centrifugal cleaners. With the improved technique, the accepts from the first stage bank of centrifugal cleaners may be combined with the accepts from the second stage bank of centrifugal cleaners and fed forward to a thickening device, for example. The technique is also suitably employed for removing stickies from material which has already been screened with a fine screen.