The pitch of a periodic tone depends on its fundamental frequency (F0), and the brightness of its timbre depends on the centroid of its power spectrum (Fc). The goal of the present study was to determine whether small shifts in F0 and in Fc are detected independently of each other. The standard tone used had an F0 of 400 Hz, five harmonics (400-2000 Hz), and a triangular spectral envelope peaking at an Fc of 1000 Hz. With a forced-choice adaptive procedure, detection thresholds were measured for (1) shifts in F0 alone (Fc being fixed), (2) shifts in Fc alone (F0 being fixed), and (3) combined shifts in F0 and Fc. The two components of the combined shifts were chosen to have the same level of detectability when presented alone. Overall, as expected from the independence model, the combined shifts were not better detected when their two components had the same direction (F0 and Fc both increase, or both decrease) than when they had opposite directions. However, substantial differences between subjects were observed with respect to the perceptual integration of shifts in F0 and in Fc.