The factors influencing the stream segregation of discrete tones and the perceived continuity of discrete tones as continuing through an interrupting masker are well understood as separate phenomena. Two experiments tested whether perceived continuity can influence the build-up of stream segregation by manipulating the perception of continuity during an induction sequence and measuring streaming in a subsequent test sequence comprising three triplets of low and high frequency tones (LHL- ⋯). For experiment 1, a 1.2-s standard induction sequence comprising six 100-ms L-tones strongly promoted segregation, whereas a single extended L-inducer (1.1 s plus 100-ms silence) did not. Segregation was similar to that following the single extended inducer when perceived continuity was evoked by inserting noise bursts between the individual tones. Reported segregation increased when the noise level was reduced such that perceived continuity no longer occurred. Experiment 2 presented a 1.3-s continuous inducer created by bridging the 100-ms silence between an extended L-inducer and the first test-sequence tone. This configuration strongly promoted segregation. Segregation was also increased by filling the silence after the extended inducer with noise, such that it was perceived like a bridging inducer. Like physical continuity, perceived continuity can promote or reduce test-sequence streaming, depending on stimulus context.