This article considers tests for (seasonal) unit roots in a univariate time-series process that are similar with respect to both the initial values of the process and the possibility of (differential seasonal) drift under the (seasonal) unit root null. In contrast to existing approaches, the technique of recursive (seasonal) de-meaning and (seasonal) de-trending of the process is adopted. Representations are derived for the limiting distributions of the proposed statistics under the (seasonal) unit root null and under near (seasonal) integration. In the nonseasonal case the asymptotic local power of the proposed test is shown to exceed that of existing tests when the initial observation is drawn from the stationary distribution of the process. The proposed tests also display superior finite sample size and power properties to conventional seasonal unit root tests and variants of such tests constructed using simple symmetric least squares and weighted symmetric least squares estimation.