The impact of an intermediate reboiler or condenser on the distillation of ideal binary mixtures into pure product streams is studied using a simplified model. The advantage of heuristics derived from this study is that they can quickly tell a process engineer if an intermediate reboiler or condenser is going to be effective in improving the efficiency and, of the two options, which one would be more effective. The heuristics simply states that if the actual fraction of liquid in a given feed is less than that with the maximum thermodynamic efficiency for distillation with no intermediate reboiler or condenser, then an intermediate condenser not only substantially improves the thermodynamic efficiency but is also more effective than an intermediate reboiler. An analogous heuristics exists for the intermediate reboiler when the fraction of liquid in the feed is greater than the optimum. Quick identification of cases that can achieve a substantial improvement in efficiency provides an incentive to search for the proper utilities needed for the intermediate reboiler or condenser. When relatively pure feed streams (concentration of either component greater than 90%) are distilled, the extremely low efficiencies of distillation can be remarkably improved by using an intermediate reboiler or condenser.