Life-history traits are expected to exhibit negative phenotypic trade-offs, but often do not. In a seminal paper, van Noordwijk and de Jong (1986) provided an answer to this seeming paradox. According to their model, trade-offs will be more difficult to detect if variation in resource acquisition (or investment) is high relative to variation in resource allocation to the traits under consideration. Despite its influence on subsequent life-history studies, this model has rarely been tested. I use data from 10 species of scorpion (a total of 30 datasets, including multiple populations or years for some species) to test the van Noordwijk-de Jong model as modified to examine the relationship between offspring size and number. For both the overall data and a subset, including only the species Centruroides vittatus, I found that the correlation between offspring size and number within a population was significantly negatively correlated with the ratio of allocation variance to investment variance. That is, strong trade-offs were found when the investment variance was low relative to the allocation variance. These results were robust to the particular measure of offspring size and to whether offspring data were adjusted for female size variation. My results therefore provide strong evidence in support of the van Noordwijk and de Jong model.