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Adaptive correction on large ground-based telescopes is enabling a variety of novel studies that would be impossible at the limits of spatial and spectral resolution imposed by the Earth's turbulent atmosphere. Even relatively high-order systems, however, do not yield a perfect correction and as a result are compromised by a low-intensity halo of remnant light that is removed from the core of the point-spread function (PSF) and dispersed in the focal plane. Worse still, this halo is neither constant in time nor uniform in position but is concentrated in transient spots that move about as mutually coherent patches of phase over the telescope aperture happen to combine constructively in the image plane. These "speckles" in the PSF set limits on ground-based searches for faint companions to bright stars. We describe here simple properties of the physics of speckle formation that will affect the statistics of residual speckles in a fundamental way: at high correction, the secondary maxima of the static PSF will coherently amplify or "pin" the time-varying speckles, influencing their effective characteristic lifetimes and dramatically changing their spatial distribution. Furthermore, as a result of speckle pinning, temporal variations in the noncommon path errors that occur in practical adaptive optics systems will cause an additional gradual drift in the spatial distribution of speckles, as Airy rings shift. Speckle pinning may be exploited to suppress speckle noise by tailoring the PSF with static aberrations artificially injected via the deformable mirror so as to clear a region of the PSF of Airy rings and hence of pinned speckles, a technique that we term "speckle sweeping."