We report electrochemical and x-ray-diffraction studies of the intercalation of lithium in graphite and in disordered carbons. The phase diagram of electrochemically intercalated graphite agrees well with previous work on samples prepared by chemical methods. The we11-known staged phases present in intercalated graphite are absent in intercalated petroleum coke. Furthermore, the voltage V(x) of Li/Li"C6 cells differs greatly when graphite or coke is used as the host. By heating coke to successively higher temperatures, we are able to increase the graphitization or crystalline order of the host in a continuous fashion and study the effect of this variation on the phase diagram of Li"C, and on V(x). We find that staged phases are suppressed at room temperature for hosts less ordered than a "critical disorder. " A lattice-gas model with random site energies is used to model the effects of host disorder and qualitatively explains the suppression of staged phases and the changes in V(x) with increasing disorder in the host. For a rectangular "density of sites, " staged phases are suppressed when the width of the site energy distribution is greater than the magnitude of the mean-field attractive Li-Li interaction, which causes island growth and staging in intercalated graphite.