Purely heat-driven refrigeration has the potential for high primary-energy efficiency, especially when powered by waste heat or solar thermal sources. This paper presents a novel expression for the ideal adsorption step location as a function of operating conditions. This methodology is then applied to a hypothetical stepwise material to evaluate its intrinsic efficiency. This analysis technique is then extended to allow facile efficiency comparisons for any adsorbent refrigerant pair using an adsorbent's isotherm and heat of adsorption properties. This work focuses on limitations to efficiency due to the equilibrium thermodynamics. It is found that a stepwise adsorbent can have a single-effect intrinsic efficiency of as high as about 85% of Carnot, assuming typical adsorbent specific heats and uptake capacity. Using these tools, we analyze the maximum ratio of cooling to heat input (coefficient of performance) for two adsorption pairs, zeolite 13X-water and UiO-66-water, which are found to have maximum coefficients of performance of 0.52 and 0.88 for a cold side temperature of 10 degrees C and an ambient temperature of 30 degrees C, respectively. Meanwhile, the maximum fraction of Carnot cooling is 37% for zeolite 13X-water and 67% for UiO-66-water. Moreover, these peak fractions of Carnot occur at much higher regeneration temperatures for 13X (196 degrees C) than for UiO-66 (60 degrees C). These two materials could be coupled in a two-stage cascading triple-effect adsorption cycle that operates with a combined coefficient of performance of 1.50 at a regeneration temperature of 196 degrees C, a cold-side temperature of 10 degrees C, and an ambient temperature of 30 degrees C.