  We consider a form of state-dependent drift condition for a general Markov
chain, whereby the chain subsampled at some deterministic time satisfies a
geometric Foster-Lyapunov condition. We present sufficient criteria for such a
drift condition to exist, and use these to partially answer a question posed by
Connor & Kendall (2007) concerning the existence of so-called 'tame' Markov
chains. Furthermore, we show that our 'subsampled drift condition' implies the
existence of finite moments for the return time to a small set.
