We present a methodology to sample signals in such a way so as to avoid the effects of signal clipping due to a limited dynamic range. We do so by attenuating a selective subset of the data before it gets sampled, so that if clipping is detected after the sampling process we can easily estimate the missing samples using the non-clipped samples that were attenuated. We show that under sparsity assumptions it is possible to reconstruct the clipped samples and recover a satisfactory representation of the original signal. We provide an analysis of the side effects of this process and show that on average when sampling signals with highly varying or unknown gain, we can guarantee a significantly lower potential for signal distortion and noise.