I build a DSGE model where households face two occasionally binding credit constraints: a loan-tovalue (LTV) constraint and a debt-service-to-income (DTI) constraint. From an estimation of the model, I infer when each constraint was binding over the 1975-2017 timespan. The LTV constraint often binds in contractions, when house prices are relatively low - and the DTI constraint mostly binds in expansions, when mortgage rates are relatively high. Moreover, both constraints unbind during robust expansions. I also infer that DTI standards were relaxed during the mid-2000s credit boom, going from a maximally allowed DTI ratio of 28 pct. in 1999 to 35 pct. in 2006. In the light of this, the boom could have been avoided by tighter DTI limits. A lower LTV limit could contrarily not have prevented the boom, since soaring house prices slackened this constraint. In this way, whether or not a constraint binds shapes its effectiveness as a macroprudential tool. The role of multiple credit constraints for the emergence of nonlinear dynamics is corroborated by county panel data.