One-bit quantization is a method of representing bandlimited signals by {+1,-1} sequences that are computed from regularly spaced samples of these signals; for each sampling density $\lambda$, convolving these one-bit sequences with appropriately chosen filters produces increasingly close approximations of the original signals as $\lambda \to \infty$. This method is widely used for analog-to-digital and digital-to-analog conversion, because it is less expensive and simpler to implement than the more familiar critical sampling followed by fine-resolution quantization. However, unlike fine-resolution quantization, the accuracy of one-bit quantization is not well-understood. A natural error lower bound that decreases like $2^{-\lambda}$ can easily be given using theoretic arguments. Yet, no one-bit quantization algorithm was known with an error decay estimate even close to exponential decay. In this talk, we present an infinite family of one-bit sigma-delta quantization schemes that achieves this goal. In particular, using this family, we prove that the error signal for $\pi$-bandlimited signals is at most $O(2^{-.07\lambda})$.