We consider the problem of designing an effective sampling scheme for sparse multi-band signals. Based on previous results on periodic non-uniform sampling (Multi-Coset) and recent advances in Compressive Sensing (CS), we propose a new sampling scheme, the Dynamic Single Branch Non-uniform Sampler (DSB-NUS). Our scheme estimates the spectral support using non-uniform spectrum sensing technique to minimize the average sampling rate, thereby reducing the number of samples as well as energy consumption. In this paper, we show through simulation results that compared to existing Multi-Coset based samplers, our proposed sampler provides superior performance, both in terms of sampling rate and energy consumption. Moreover, we show that our proposed sampler is not constrained by the inflexibility of hardware circuitry and is easily reconfigurable.