A bandgap reference circuit utilizes differential transistors to generate a temperature-independent bandgap voltage. In place of conventional trim elements that are connected in parallel to and adjust the resistance values of the bandgap reference circuit, current control circuits are placed in the current paths passing through the differential transistors (i.e., connected to the critical nodes located at the terminals of the differential transistors). Each current control circuit includes a resistive "trim" element (e.g., a zener diode) and associated trim pads that are separated from the critical nodes (i.e., the terminals of the differential transistors) by isolation transistors such that, during a trim/test procedure, the stray capacitances introduced by trim/test equipment probes are prevented from altering the performance of the bandgap reference circuit. In one embodiment, a current control circuit is connected to the critical node connected to the base of at least one of the differential transistors.