We present three new stopping rules for Multistart based methods. The first uses a device that enables the determination of the coverage of the bounded search domain. The second is based on the comparison of asymptotic expectation values of observable quantities to the actually measured ones. The third offers a probabilistic estimate for the number of local minima inside the search domain. Their performance is tested and compared to that of other widely used rules on a host of test problems in the framework of Multistart.