Increasing diversity is often advocated as an effective strategy through which higher education systems can cope with the new functions that they are required to perform, and respond to the varied demands that they face from an increasing and more diverse set of stakeholders. Such diversity is sometimes considered as the "natural" outcome of intensified competition among institutions. Using Italian data relative to the period 1999/2000-2005/2006, and focusing on one specific dimension of diversity--the universities' horizontal differentiation in terms of disciplines taught--the paper shows empirically how the introduction of measures directed at strengthening competition in higher education can actually contribute to a reduction in the system's overall diversity, as universities attempt to boost enrolments by increasing their specialization in more popular disciplines. The diversity-enhancing property of increased competition should not therefore be taken for granted, even with respect to other features of higher education systems.