It has been assumed that intermediate-mass black holes (IMBHs) in globular clusters can only reside in the most centrally concentrated clusters, with a so-called `core-collapsed' density profile. While this would be a natural guess, it is in fact wrong. We have followed the evolution of star clusters containing IMBHs with masses between 125 \le M_{BH} \le 1000 M_{\odot} through detailed N-body simulations, and we find that a cluster with an IMBH, in projection, appears to have a relatively large `core' with surface brightness only slightly rising toward the center. This makes it highly unlikely that any of `core-collapsed' clusters will harbor an IMBH. On the contrary, the places to look for an IMBH are those clusters that can be fitted well by medium-concentration King models. The velocity dispersion of the visible stars in a globular cluster with an IMBH is nearly constant well inside the apparent core radius. For a cluster of mass M_C containing an IMBH of mass M_{BH}, the influence of the IMBH becomes significant only at a fraction 2.5 M_{BH}/M_C of the half-mass radius, deep within the core, where it will affect only a small number of stars. In conclusion, observational detection of an IMBH may be possible, but will be challenging.

13 pages, 3 figures, Accepted ofr publication in ApJ (scheduled for February 2005)