A rapid passage of He-4 through the lambda (superfluid) transition is expected (W.H. Zurek, Nature 317, 505; 1985) to result in the production of topological defects (quantized vortices) through the Kibble mechanism, the same process that is believed to have produced cosmic strings at the GUT phase transition of the early universe. But recent experiments (Dodd et al, Phys. Rev. Lett. 81, 3703; 1998) show that the density of vortices created, if any, seems to be smaller than predicted by a factor of at least 100. Possible ways of improving the sensitivity of the exoperiment are discussed.