During an encounter between a noble-gas atom and an alkali-metal atom, the electron density at the alkali nucleus is altered, resulting in a collisional change in the alkali's hyperfine coupling (i.e., AI.S-->(A+deltaA)I.S). In the case of binary encounters, this process has been termed the Carver mechanism. The short-lived collisional change in hyperfine coupling can have very noticeable effects: it plays an important role in the loss of nuclear spin polarization in high magnetic fields, and it can be one of the dominant line broadening mechanisms for alkali hyperfine transitions (e.g., in atomic clocks). Unfortunately, though there have been measurements of the Carver relaxation rate, to date there has been little theoretical analysis of the Carver mechanism, in large part due to the very difficult problem of computing deltaA. In the present work, the author develops a theory of the Carver rate based on a semiempirical expression for deltaA(r)/A, where r is the internuclear alkali/noble-gas separation, and validates the theory by comparing to experiment. This model is then used to compute Carver and Bouchiat relaxation rates (i.e., the three-body sticking-collision analog of the Carver rate) in diverse/alkali-noble gas systems. The main conclusion of this work is that Carver rates vary by orders of magnitude across the alkalies, and in general will likely only play a significant role for Rb and Cs noble-gas systems.