  We perform a detailed study of the Hegselmann-Krause bounded confidence
opinion dynamics model with heterogeneous confidence $\varepsilon_i$ drawn from
uniform distributions in different intervals $[\varepsilon_l, \varepsilon_u]$.
The phase diagram reveals a highly complex and nonmonotonous behaviour, with a
re-entrant consensus phase in the region where fragmentation into multiple
distinct opinions is expected for the homogeneous case. A careful exploration
of the phase diagram, along with an extensive finite-size analysis, allows us
to identify the mechanism leading to this counter-intuitive behaviour. This
systematic study over system sizes which go well beyond those of previous
works, is enabled by an efficient algorithm presented in this article.
