In this paper, the authors propose a new constraint governing the syntactic operation of Quantifier Raising (QR), on the basis of data from English. The empirical core of the paper is focused on the availability of QR out of infinitives, the acceptability of which is shown to be variable across different types of infinitive clause. In order to explain this variability, the authors argue that QR out of infinitives is in principle possible, unless the covertly-moved quantifier crosses a c-commanding (overt) DP or adjunct, such as an experiencer. This is dubbed the intervention constraint. In the second half of the paper, the authors show how the intervention constraint can be marshalled to provide a uniform explanation for a range of hitherto mysterious constraints on QR, such as the Reconstruction Requirement on inverse scope, and scope freezing in the double object construction.