We present results of infrared observations of Neptune from the 10-m W. M. Keck I Telescope, using both high-resolution (0.04 arcsecond) broadband speckle imaging and conventional imaging with narrowband filters (0.6 arcsec resolution). The speckle data enable us to track the size and shape of infrared-bright features ("storms") as they move across the disk and to determine rotation periods for latitudes -30 and -45°. The narrowband data are input to a model that allows us to make estimates of Neptune's stratospheric haze abundance and the size of storm features. We find a haze column density of ̃10 6 cm -2 for a haze layer located in the stratosphere, and a lower limit of 10 7 cm -2 and an upper limit of 10 9 cm -2 for a layer of 0.2 μm particles in the troposphere. We also calculate a lower limit of 7×10 6 km 2 for the size of a "storm" feature observed on 13 October 1997.