During the last few years, the number of university students choosing to follow engineering degrees has decreased dramatically in Spain. For that reason, several university departments, in collaboration with some high schools, have developed a range of activities in order to promote a higher enrollment rate, to improve the level of mathematics and physics that students have when entering university, to explode the myth of engineering degrees being difficult studies not within everyone's reach, and to rationalize the curricula of engineering degrees, coordinating all their courses and directing them toward the global objectives of the degree. In this paper, the results of an Outreach Project for Engineering Education (OPEE) comprising four successful activities developed over the last decade at the Higher Technical School of the University of Cordoba, Spain, are reported. Most important is that in the face of the significant decrease of the amount of engineering first-year students observed in Spain in general, and Cordoba in particular, enrollment in the Higher Technical School of the University of Cordoba has remained constant. (Contains 2 tables and 5 figures.)