Among the factors affecting the solar radiation that reaches the ground, clouds play a key role in its short-term variability causing events ranging from almost total reduction to substantial enhancements under particular conditions. The purpose of this paper is to detect and to analyze the enhancement events on total solar horizontal irradiance at Granada (Southeastern Spain) using one-minute data during a study period of five years (January 2006 to December 2010). For this goal, an empirical model for cloud-free conditions has been used together with information on cloud cover (i.e., oktas) provided by a sky camera. Around 6% of the one-minute data were classified as enhancements, but only those episodes with duration longer than 5 min were studied. For all these episodes, the relative increases over the expected cloud-free values were, on average, 13.5%, reaching maximum values up to 50%. The enhancement episodes were related to broken-cloud situations (2–7 oktas) without prevalence for a particular number of oktas. The analysis of the seasonal distribution of those events showed that ~50% of them occur in spring, followed distantly by the other seasons with percentages below 20%. Additionally, a long enhancement event (74 min) was analyzed in detail, showing the relevant role of the diffuse component in this event. Finally, extreme enhancements (those episodes with surface solar levels higher than their extraterrestrial value) were also reported, consisting in 0.14% of the one-minute data. They occurred only under heavy cloudy situations (6–7 oktas), showing relative increases between 30% and 60% with respect to expected cloud-free conditions.