We present a simple analysis of the time variations of several optical spectral characteristics for a sample of optically very faint, infrared-selected, extreme carbon stars. This analysis yields estimates of stellar periods that show these dust-embedded stars to be long-period (similar to 1.5 yr) Mira variables. We have not found any ECS analogous to the extremely long-period OH/IR stars: the longest ECS period is similar to 2 yr. We explore the relationships between amplitude of variation of H alpha emission and its mean level, and discuss the likelihood that some ECS dust shells are disklike rather than spherical. We investigate the relative phasing of the cycles of H alpha, sodium absorption, optical continuum colors, and infrared photometric variations. The combination of optical, near-infrared and IRAS photometry permits estimates to be made of both stellar distance and circumstellar extinction, through the bolometric luminosity. (C) 1996 American Astronomical Society.