In this talk we will explore parameter spaces of meromorphic maps with finitely many singular values. We will list various types of parameters for which the orbits of one or more singular values have peculiar characteristics, for example, are preperiodic, converge to a parabolic cycle, or are truncated after a certain number of iterates. We will look at the relations between such parameters and show that several of these types of parameters are dense in the bifurcation locus. To do so we will need to implement new strategies with respect to the rational case. This is joint work with N. Fagella and M. Astorg.