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We discuss a quantum-metrology protocol designed to estimate a physical parameter in a {Bose-Einstein} condensate of N atoms, and we show that the measurement uncertainty can decrease faster than {1/N.} The {1/N} scaling is usually thought to be the best possible in any measurement scheme. From the perspective of quantum information theory, we outline the main idea that leads to a measurement uncertainty that scales better than {1/N.} We examine in detail some potential problems and challenges that arise in implementing such a measurement protocol using a {Bose-Einstein} condensate. We discuss how some of these issues can be dealt with by using lower-dimensional condensates trapped in nonharmonic potentials.