For stability, the replication of unit-copy plasmids ought to occur by a highly controlled process. We have characterized the replication dynamics of a unit-copy plasmid F by a replication rate function defined as the probability per unit age interval of the cell cycle that a plasmid will initiate replication. Analysis of baby-machine data [J. Bacteriol. 170 (1988) 1380; J. Bacteriol. 179 (1997) 1393] by stochastics that make no detailed reference to underlying mechanism revealed that this rate function increased monotonically over the cell cycle with rapid increase near cell division. This feature is highly suggestive of a replication control mechanism that is designed to force most plasmids to replicate before cells undergo division. The replication rate function is developed anew from a mechanistic model incorporating the hypotheses that initiators are limiting and that steric hindrance of origins by handcuffing control initiation of replication. The model is based on correctly folded initiator protein monomers arising from an inactive dimer pool via chaperones in limiting amounts, their random distribution to high affinity sites (iterons) at the origin (ori) and an outside locus (incC), the statistical mechanics of bound monomer participation in pairing the two loci (cis-handcuffing), and initiation probability as proportional to the number of non-handcuffed ori-saturated plasmids. Provided cis-handcuffing is present, this model closely accounts for the shape of the replication rate function derived from experiment, and reproduces the observation that replication occurs throughout the cell cycle. Present concepts of iteron-based molecular mechanisms thus appear capable of yielding a quantitative description of unit-copy-number plasmid replication dynamics.