The strength and number of nicotinic synapses that converge on secretomotor B neurons were assessed in the bullfrog by recording intracellularly from isolated preparations of paravertebral sympathetic ganglia 9 and 10. One input to every B neuron invariably produced a suprathreshold EPSP and was defined as the primary nicotinic synapse. In addition, 93% of the cells received one to four subthreshold inputs that were defined as secondary nicotinic synapses. This contradicts the prevailing view, which has long held that amphibian B neurons are singly innervated. More important, the results revealed that B cells provide the simplest possible experimental system for examining the role of secondary nicotinic synapses on sympathetic neurons. Combining the convergence data with previous estimates of divergence indicates that the average preganglionic B neuron forms connections with 50 ganglionic B neurons and that the majority of these nicotinic synapses are secondary in strength. Secondary EPSPs evoked by low-frequency stimulation ranged from 0.5 to 10 mV in amplitude and had an average quantal content of 1. Nonetheless, secondary synapses could trigger action potentials via four mechanisms: spontaneous fluctuations of EPSP amplitude, two-pulse facilitation, coactivation with other secondary synapses, and coactivation with a slow peptidergic EPSP. The data were used to formulate a stochastic theory of integration, which predicts that ganglia function as amplifiers of the sympathetic outflow. In this two-component scheme, primary nicotinic synapses mediate invariant synaptic gain, and secondary nicotinic synapses mediate activity-dependent synaptic gain. The model also provides a common framework for considering how facilitation, metabotropic mechanisms, and preganglionic oscillators regulate synaptic amplification in sympathetic ganglia.