A hot swap controller includes a shunt resistor (32-1,2) and a power transistor (37-1,2) having a source coupled to a load maintains the first power transistor in a fully-turned-on condition to cause it to deliver a load current contribution (I1,2) which flows through the shunt resistor and the power transistor to the load (25). Current sensing circuitry (35-1,2) produces a first control signal (V45-1,2-V47-1,2) equal to the difference between a DC component (V47-1) proportional to a first load current contribution (IL1) flowing in the first shunt resistor and a feedback-based component (V45-1). A control amplifier (49-1,2) produces a second control signal (V51-1,2) in response to the first control signal to modify a drive signal (53-1) to the power transistor so as to reduce a channel resistance of the power transistor if the first control signal exceeds a predetermined level.