This article contains an analysis of a version of the well-known inhibitor-dilution model for the control of initiation of chromosome replication in bacteria. According to this model, an unstable inhibitor interacts with an initiation primer in a hit-and-destroy fashion to prevent successful initiation; both constituents are presumed to be RNA species that are synthesized constitutively. The model further postulates that the inhibitor interacts cooperatively with the primer, that the inhibitor gene is removed some distance from the origin of replication, and that an eclipse period exists during which the chromosome origin is not able to reinitiate. This unstable-inhibitor version is characterized by four parameters: the inhibitor half-life, the cooperativity index, the location of the inhibitor gene, and the eclipse period; computer simulations are used to study the effect of each of these on the DNA and interdivision time distributions in exponentially growing steady-state cultures. In neither case was any combination of parameter values found that could provide even moderately satisfactory agreement between the simulation results and experimental data. From the examples furnished and the associated discussion, it appears that there are none--that no combination of parameter values exists that can reasonably be expected to produce a significantly better fit than those tested. We conclude that the model in its present form cannot be a valid description of chromosome replication control in bacteria. It is pointed out that this does not necessarily apply to negative initiation control models in general, or even to all inhibitor-dilution systems, merely to the particular ColE1-like mechanism considered here. Nevertheless, recent experimental results, which can only be understood in terms of a very high degree of initiation synchrony within individual cells, offer strong evidence against stochastic models of this kind for the control of chromosome replication.