In this paper we study structured Pc1 pulsations (also called Pc1 pearls) observed on ground, concentrating on the relation between the pearl repetition period &tgr; and the wave frequency f. Earlier studies suggest that the product &tgr;f is roughly constant. We reexamine this relation and show that a simple inverse law is excluded. Instead, our observations suggest the relation &tgr;∝f-p, with p=0.59¿0.06, posing a new, strict constraint on theories of Pc1 pearl formation. We also study the L dependence of various combinations of &tgr; and f using a model L value and extract additional constraints from these combinations. We discuss these constraints in the bouncing wave packet model of pearl formation and determine the range of allowed parameter values in this model. We present two models of energetic ions with different L distributions and show that one of them can be excluded by the constraints derived. We also discuss how to further improve on these constraints to better test the bouncing wave packet model and other theories of Pc1 pearl formation. ¿ 1999 American Geophysical Union