Deliberative Transformative Moments (DTM) is a new concept that serves as an amendment to the DQI. With this new concept it is easier to get at the quick give-and-take of discussions of small groups of ordinary citizens. As an illustration, we apply the concept to discussions about the peace process among Colombian ex-combatants, ex-guerrillas and ex-paramilitaries. Specifically, we show how personal stories can transform a discussion from a low to a high level of deliberation and how they can have the opposite effect. To increase the level of deliberation in the general population, we recommend that good illustrations of DTM’s should be part of the school programs from an early age on, so that children learn how to discuss with others who have different opinions and values.