We analyze an empirically important issue with recursive right-tailed unit root tests for bubbles in asset prices. First, we show that serially correlated innovations, which is a feature that is present in most financial series used to test for bubbles, can lead to severe size distortions when using either fixed or automatic (based on information criteria) lag-length selection in the auxiliary regressions underlying the test. Second, we propose a sieve-bootstrap version of these tests and show that this results in tests which control size well across a number of simulation designs both with and without highly autocorrelated innovations. We also find that these improvements in size come at a relatively low cost for the power of the tests. Finally, we apply the bootstrap tests on the housing market of OECD countries, and generally find much weaker evidence of housing bubbles compared to existing evidence.