We consider the problem of non-adaptive noiseless group testing of $N$ items of which $K$ are defective. We describe four detection algorithms: the COMP algorithm of Chan et al.; two new algorithms, DD and SCOMP, which require stronger evidence to declare an item defective; and an essentially optimal but computationally difficult algorithm called SSS. By considering the asymptotic rate of these algorithms with Bernoulli designs we see that DD outperforms COMP, that DD is essentially optimal in regimes where $K \geq \sqrt N$, and that no algorithm with a nonadaptive Bernoulli design can perform as well as the best non-random adaptive designs when $K > N^{0.35}$. In simulations, we see that DD and SCOMP far outperform COMP, with SCOMP very close to the optimal SSS, especially in cases with larger $K$.