Many instrumental variable (IV) regressions include control variables to justify (conditional) independence of the instrument and the potential outcomes. The plausibility of conditional IV independence crucially depends on the timing when the control variables are determined. This paper systemically works through different IV models and discusses the satisfaction of conditional IV independence when controlling for covariates measured (a) prior to the instrument, (b) after the treatment, or (c) both. One finding is that (b) identifies causal effects only in restrictive models that generally rule out direct effects of pre-instrument covariates on the outcome and confounding of post-treatment covariates, which may jeopardize the usefulness of IV estimation in cross sectional data. A further finding is that identification under (a) to (c) is generally lost if post-treatment covariates are confounded and a function of the instrument. An empirical application using the Vietnam War draft risk as instrument either for veteran status or education to estimate the effect of these variables on health outcomes illustrates these identification issues.