Shot noise measurements have been used to measure the charge of quasiparticles in the fractional quantum Hall (FQH) regime. To induce shot noise in an otherwise noiseless current of quasiparticles, a barrier is placed in its path to cause weak backscattering. The measured shot noise is proportional to the charge of the quasiparticles; for example, at filling factor v=1/3, noise corresponding to q=e/3 appears. For increasingly opaque barriers, the measured charge increases monotonically, approaching q=e asymptotically. It was therefore believed that only electrons, or alternatively, three bunched quasiparticles, can tunnel through high-potential barriers encountered by a noiseless current of quasiparticles. Here we investigate the interaction of e/3 quasiparticles with a strong barrier in FQH samples and find that bunching of quasiparticles in the strong backscattering limit depends on the average dilution of the quasiparticle current. For a very dilute current, bunching ceases altogether and the transferred charge approaches q=e/3. This surprising result demonstrates that quasiparticles can tunnel individually through high-potential barriers originally thought to be opaque for them.